I'm no expert, but I'll provide my opinion about some of your concerns.
I figured 4 squads of 4 would be logical (probably my first mistake) with two squads for melee and two squads of marksdwarfs. After some fitzing about I figured out how to create the four squads and set them up. Right now I have very minimal armor and clothing in the fort, but jobs are queued up.
You'll want to decide on how you intend to train up these soldiers as well. If you opt to have them spar and train to become competent soldiers, consider using smaller squads. Lots of people advise squads of two, as that apparently encourages sparring.
Personally, I set up a danger room and put the little fellas through hell for a season or two and then let them loose on the world.
Once you decide to set up uniforms, be sure to replace clothing instead of having them put on armor over clothing. In my experience, that simplifies things.
I have a barracks built, with 10 beds, a couple armor racks and a weapon rack around the edges.. plenty of open space in the middle. 10 archery targets have been built with channels behind. Several hundred wooden bolts have been created for practice (I just started butchering, bone coming soon).
That sounds like more than enough space for your guys to do their thing. If you're using totally untrained marksdwarfs you may not see much activity at the ranges. Before putting together a squad of marksdwarfs, I set up a big group of hunters. Once they have some skill, I remove the hunting labor and then enlist those dwarfs. That seems to make them more inclined to target practice.
So, now I am faced with training and scheduling. From what I understand squads can be training, on patrol or idle, right? I would like to always have some military on patrol at all times (shouldn't I?) with some time spent training and the rest working on civilian skills? Right? I guess ideally I would have one melee squad and one crossbow squad on patrol at all times?
You can certainly schedule them this way if you like. Once I put dwarfs in the military, that's all I have them do. They'll get bad thoughts about long patrol duty, but that hasn't resulted in tantrums in my forts yet.
Or, do I just alternate between train and idle right now, and start patrolling when I get some more squads set up?
There's an opportunity cost here I think. If they're patrolling and are very low skill, they may get wiped out quickly. On the other hand, if they're patrolling and kill some local wildlife or take out a thief, that will develop skill. If your dwarfs mingle a lot in common areas and these soldiers start biting the dust, expect problems.
How do I coordinate scheduling? If I switch between train, idle and patrol it seems like I might need 3 sets of squads, each squad doing each task 4 months of the year.
I'm running six squads at present, four melee and two ranged, and they switch off patrolling and defending burrows. I have my ranged guys patrol and defend from the walls rather than on the ground. My melee guys are just keeping watch at the front gate now, with each order set to a minimum of three soldiers. With that set up, I've always got a handful of soldiers at the gate, and they take breaks, sleep, etc. without needing direct oversight.
Am I just setting myself up for failure here, or is this a good plan?
Seems like a fine plan to me. At this point, I think you'll just need to decide how you'd like to begin developing their skills.