Just to explain the upgrade system a bit because I enjoy doing these things and someone is actually listening now.
Let's look at the starter ice wand. Wiki page is
here, open it up, scroll down to the upgrade table.
First some simple facts, you can normally upgrade a weapon five times. For the purposes of remaining consistant with the wiki, these slots are 0 1 2 3 4, so 0 is the first slot, etc. I hate how the wiki numbers these things but hey consistancy. The only way to remove an upgrade is artisan upgrade removal kits, and even then they will only remove artisan upgrades. I'll explain them seperately, as they are VERY SPECIAL!
So, on the table it's mostly self explanatory except for "UG#". That's the upgrade slots that upgrade can take. So the first upgrade on the list, "Ice elemental resonance" can go in the first three slots. You'll need to upgrade it three seperate times if you want it to take up all three, every seperate upgrade only takes up one slot. You go to the respective NPC(s) in the NPC column, click the upgrade button in their dialogue, and then find the upgrade. Sometimes the upgrade names in the wiki aren't consistant with the english names for whatever reason, so just look at the stats if you can't find the name. You pay them some gold, it uses up some proficiency (22 for example with ice elemental resonance), and walla upgraded wand. So despite 100 prof being the maximum prof for gear, you may well need more then that to upgrade it all the way. Upgrades can be done in different sessions obviously. Upgrades DO NOT raise repair cost or change anything that they do not explicitly state they are changing.
Those are basic upgrades. Artisan upgrades are like them BUT there are usually only a few NPCs that can do them, they usually cost an metric ton of gold, they always use 100 prof, they always take up the last normal upgrade slot, and they randomly roll the stats. So for beginner ice wand...
It will first roll to apply any of these stats at all. It's not possible to get an artisan upgrade that applies nothing (I think) but it's entirely possible you could blow all your money on an ice wand artisan upgrade and get +5 int and nothing else. Underwhelming to say the least.
Second, it will roll the stats that did get applied and see what value they end up at. So for instance it's possible for it to roll up to +80 intelligence which is quite a huge amount of intelligence.
So the best possible artisan upgrade for an ice wand is +80 intelligence +5 HP and +5 MP.
Next up, gem upgrades. The gem upgrade table is below the normal upgrade table. You can only apply a gem upgrade after all five normal upgrades are done. Gem upgrades will typically raise max durability or do some other random thing. Some upgrade chains will end with very low max dura so it largely depends on where you want your dura at.
Gem upgrades always use 100 prof, and need 3 gems. In the case of the Ice Wand Gem Upgrade 1 you need a garnet of at least 1 cm, a ruby of at least 2 cm, and an aquamarine of at least 4cm. The gem requirements will change between upgrades and weapons.
After gem upgrades is the final stop, special upgrades. These are universal between weapons, and these are what you're missing out on with your beginner wand. They're not bad, but definitely something you get later on when you're more well established, and a cheap repair wand is always nice to have.
Special upgrades need upgrade stones. They're rare drops from high end dungeons, events, ancients, and generally everything that is hard-ish to do. They come in two varieties, Red, which raises critical rate, and blue which raises min-max damage (it raises your magic attack by a percentage in the case of a wand). You can only apply one color to any given weapon. Both of these do different things to cylinders, if you want to know more about that (or specific numbers) go
here, they're in the tables.
That's about it for special upgrades, with one catch. Normally a failed special upgrade will drop it's special upgrade level by one, so ou have to do it again. BUT, if you special upgrade from 5 to 6, it will be destroyed instantly. So.... don't do that.