Ideally the former and the latter would have the same results, but this being dwarf fortress I suppose it's best not to make that assumption. I just did up a uniform, which I titled "Basic Kit," and on this uniform I assigned the following items:
I might have the equipment order wrong for some of the other items (for proper layering concerns), since this is from memory rather than from referencing the game; but, the point is that the shields are listed first, then the crossbows, then the axes. Once you have created your uniform, make sure to set it to (r)eplace civilian clothes, and then select the squad to which you want to assign this uniform. Hit (e)quip once that squad is selected, then hit Assign (U)niforms; then, select any dwarf in the squad; then, select the particular uniform, in my example, "Default Kit," and then hit Shift+Enter to assign that uniform to the entire squad. As you point out, there are concerns that the equipment might not get put on in the right order for any number of reasons: Urist McAxelord might put on part of his uniform, then suddenly decide to take a nap, or whatever. My response here isn't about how to make sure that the dwarfs wear the equipment in the right order: it is to tell you the right order that the equipment needs to be worn in order for you to get the results you want.
The short and simple version here is that, on your dwarf's inventory screen, the shields should appear above the crossbows, and the crossbow should appear above the battle axes. Once you have your dwarfs equipped such, they will alternate between using their battle axes, shield bashes, kicks, bites, and crossbow bashes in melee, with significant preference given to the battle axes. A quick way to see if you've equipped your dwarfs correctly, without going through the headache of checking the order of every individual item, is to have one of them go into a danger room and just wait a bit to see whether he becomes an Axedwarf/Axe Lord or a Hammerdwarf/Hammerlord. Equipped the right way, dwarfs will gain skill in both Axe and Hammer, but will gain skill in Axe faster than Hammer.
If you really want to be super sure that you did things right, click the spoiler for a step by step guide.
Step 1. Escape out of any screens, then hit (z): status. Go to the stocks, and navigate down to one of the clothing options: headwear, bodywear, legwear, footwear, handwear. Ensure that in at least one of these categories, there is a type of clothing item that has as many free units as dwarfs you wish to equip; for example, if you want to equip six dwarfs, make sure there are six free shirts, or trousers, or cloaks, or whatever. If you do not have at least that many clothing items available, buy or create some then come back to this guide. I will refer to this item as, "S1 clothing," throughout this guide.
Step 2. Escape out of any screens, then hit (m)ilitary. Hit (u)niforms, then hit (c): add uniform, and (N)ame this uniform whatever you like. I will refer to this uniform as, "S1 Naked," throughout this guide. Using the hotkeys visible on this screen, add the "S1 clothing item" to "S1 Naked," and do not add anything else. Make sure to also hit (r)eplace civilian clothes.
Step 3. Escape out of any screens, then hit (m)ilitary. Hit (u)niforms, then hit (c): add uniform, and (N)ame this uniform whatever you like. I will refer to this uniform as, "S1 Uniform," throughout this guide. Using the hotkeys visible on this screen, add whatever uniform items you are going to use for the squad's combat uniform, and make sure you equip everything in the right order. I am not going to walk you through permit, size, shape, and other things specific to armour items: that is a guide unto itself. Just make sure that you assign the "shields," before the "crossbows," in the list, and the "crossbows," before the "battle axes," in the list. To my knowledge the optimal choices for each of these would be adamantine shields, platinum crossbows, and adamantine battle axes, but the material is not relevant to this guide.
Step 4. Escape out of any screens, and find a place where your dwarfs will do their changing between the two uniforms you have created and any civilian clothes they might have. Make sure that this space can be sealed off completely from the rest of your fortress, such as with a door. You are going to define two burrows and two stockpiles in this area. I will call them "B1," "B2," "P1," and "P2," in this guide. Define an armor stockpile, "P1," which will only hold the specific "clothing item," that you chose for "S1 Naked," perhaps whatever other clothes your future military dwarfs are wearing.
Step 5. Define the first burrow, "B1," to cover the first stockpile, "P1," and assign your future military dwarfs to this burrow. Wait a little bit for any hauling necessary to put the necessary quantity of "clothing item," in the stockpile, "P1," and visually check to make sure you have the minimum number you need before proceeding to Step 6.
Step 6. Remove any labors that your military dwarfs might have, and they should go to B1 unless they are injured or trapped somewhere else at the time. If either of these is the case, then either fix those dwarfs or pick different ones. The purpose of B1 and P1 is so that you can order your dwarfs to go directly to that stockpile and limit the things they can interact with to only those things in that stockpile.
Step 7. Escape out of any screens. Go to the (m)ilitary screen, and add the dwarfs in B1 to a squad, which I will call in this guide "S1," but which you can name whatever you like. If you do not have a squad, create one; if you do not have a militia captain or a militia commander, assign one from the nobles screen, then create the squad, then assign the dwarfs to it.
Step 8. Assign the uniform, "S1 Naked," to the squad, "S1," by first going to the (e)quip screen, and then selecting (U): Assign Uniform, and making sure you use Shift+Enter rather than Enter to assign the uniform to the entire squad.
Step 9. Escape out of any screens. Go to the (m)ilitary screen, then to the (s)chedule screen, and make sure the squad, "S1," is set to Training for the present month. You should probably just set them to train every month while you're at it. You should also probably break up that training order to include multiple orders for a minimum of two dwarfs, but the reasons why are beyond the scope of this guide. While you are in the schedule screen, set your orders for dwarfs to (u): Inactive = Uniformed. This last bit should prevent the dwarfs from ever equipping civilian clothes, which might potentially mess up your equipment order for armours.
Step 10. Escape out of any screens and unpause the game if necessary. Open the (s)quads interface, and make sure the squad status for the squad, "S1," is set to (t)raining/active. The dwarfs in the squad, "S1," should dump what they are wearing and put on the uniform, "S1 Naked," consisting of one "clothing item" for each dwarf.
Step 11. Escape out of any screens and select (v)iew, and then visually check the (i)nventory of each of your military dwarfs to guarantee that he is only wearing the single "clothing item" from the uniform, "S1 Naked," and nothing else. If he is wearing anything else, then you will need to create a garbage dump activity zone within the first burrow, "B1," and order the individual items he has equipped to be dumped. Proceed to step 12 only after the dwarfs are properly equipped with only the single "clothing item," from the uniform, "S1 Naked," to guarantee no problems.
Step 12. Define a second armor stockpile, "P2," within your equipment changing area, and set it to only accept the specific types and materials of items you have designated for your combat uniform, "S2 Uniform," and wait for your haulers to deliver the items. Proceed to step 13 only after you have ensured that all equipment necessary to fully outfit your squad, "S1," in their combat uniform, "S1 Uniform," at which point you may also lock the door to the equipment changing area.
Step 13. Define your second burrow, "B2," such that it encompasses both your first stockpile, "P1," and your second stockpile, "P2," and assign your military dwarfs, "S1," to this second burrow.
Step 14. Escape out of any screens, and go to the (m)ilitary screen. Assign the combat uniform, "S1 Uniform," to the squad, "S1," and then unpause the game. Your military dwarfs should now dump their "clothing item," from the uniform, "S1 Naked," and equip the items from the uniform, "S1 Uniform," in the proper order.
Double check that your dwarfs are properly equipped. If you followed the steps in this guide correctly, then the (i)nventory list for each dwarf should be functionally identical: the only differences for each dwarf should be the quality of the items equipped, but their order in the (i)nventory should be identical. If for some reason your dwarfs have not equipped things in the right order, then depending on how you layered their armour this might cause some things to simply not be equipped or to be ineffective. For the purpose of ensuring that your marksdwarf squad uses their axes (or spears or swords), rather than their crossbows, in melee, the only relevant concern is that the shields appear before the crossbows, and that the crossbows appear before the edged melee weapon.
If you try this guide a few times, and it still leaves you with half-equipped dwarfs, then an even more elaborate method is to create a series of uniforms, where the first contains the first item you want your dwarfs to equip, e.g., a steel helm, the second contains both the first item and the second item, e.g., a steel helm and a leather hood, and so on, with each sequential uniform having one more item, until your final uniform is what you want the dwarfs to wear. You would then, over the course of several in-game months, slowly order the dwarfs to shift from one uniform to the next in the list, until eventually you end up with something like the uniform I described earlier in this post for my own military dwarfs.
If you're still lost, then I cannot help you.