That's the right kit, the Taylor K-2006. You MIGHT have been able to get it for $20 cheaper but over this year alone it will save you that many times over. The main tests you'll use are:
FAS-DPD for FC and CC
pH
T/A (total Alk)
CYA (Stabilizer)
CH (hardness)

I think they have an acid and base demand tests as well but you won't need to worry about them much, if at all.

Since you have a vinyl pool you'll probably not need to run the CH test more than once or twice during and ONLY if you suspect your calcium levels are too high. I run it at the beginning of the season for a baseline, but only occasionally run it a second time during the summer.

So go ahead and use your new kit! BTW, the FAS-DPD needs only enough powder to turn the solution red. More does nothing. If one scoop is enough, it's enough.
Post results for:
FC
CC
pH
T/A
CYA
CH