You'll do fine
Insulin syringes are really tiny but you'll get use to them, you can buy a pair of reading glasses (even if you do not need them) to use as magnifying glass, that way you can see the marks better and have your hands free.
Does your syringes have the half unit marks? if not try and get the ones with half unit marks because they will simplify dosing a lot. BD is the ones I use because they are the only ones I can get where I live with half unit marks on them and they have worked just fine for me, but if you live in the US there are some other brands.
Test before you shoot and if you can two hours after you shoot that way you can see how he's reacting and go from there, is hard to know how fast he's going to drop or maybe specially the first day he could not drop at all (each cat is different) and he could start dropping when the depot forms you will have to learn how he reacts.
Have your hypo kit ready (
http://www.felinediabetes.com/FDMB/threads/how-to-treat-hypos-they-can-kill-print-this-out.15887/) odds are you won't need it but is better to be prepared and remember that the take action with the Alpha track is 68
In any case post your results in the forum, since you are going to be using Lantus post in the lantus forum where there's a lot of people that can help you this is the link (
http://www.felinediabetes.com/FDMB/forums/lantus-basaglar-glargine-and-levemir-detemir.9/)
Also remember that Lantus requires consistency so you will hold the 1 unit dose at least for one week because you are just starting, unless he goes under 90 because then you will have to lower the dose in 0.25 units in which case you can post on the forum and ask what to do.