Hello,
I am myself not very good at the game, so i would recommend waiting for better advice, but i will try anyway
"Are there any tips for gaining veterancy on units? For example, anything I should be mindful about"
From what i noticed, dealing damage to vehicles gives more veterancy than dealing damage to infantry, so use that to your advantage if you can (but don't focus too much on it, veterancy will come at one point anyway)
Is veterancy that important in this game?
In my opinion, veterancy is very important (keep in mind i'm not that good)
I'd say trying to kill a vet 2/3 unit with a non-vetted/vet1 one is dangerous if the units are supposed to be similar in effiency (unupgraded cons/grens for example)
On the other hand, a vet1 unit isn't that much more dangerous in a direct fight, because most of the time vet1 gives an ability and not a direct stat bonus
Keep in mind the ability can still be a danger (spamming tripwire flares with cons everywhere can be very effective but only works for vet1 conscripts, and if your ennemy walks in them)
Should I take the time to learn the different bonuses of every units? Why?
I would say learning them isn't important, but again i'm not really a good player so don't trust me.
I'd say some are still important to know, mostly for yourself.
For example, engineers get neat veterancy bonuses, like more repair speed (at vet 2 for most i think) and don't take additional damage while repairing (vet 3 for most?)
Again, this is all coming from a noob so i would recommend waiting for more experienced/informed players to answer