First off lets clarify something:

and showed me how to set new pins to match the existing key

If you actually used a follower to remove the core and literally removed pins from the lock and then put new pins in, you can ignore the rest of this comment and go ahead and purchase that kit with no worries and more power to you.

If instead that all sounded like gibberish and what you did looked more like this then you need to understand that has absolutely nothing to do with rekeying a lock with actual pins (like you would do with the kit you linked) and you should still consider yourself to be a complete novice with zero experience in rekeying locks.

With that out of the way, the kit you linked is pretty overkill for a novice so unless you have money to burn you can just get a little kit like this for a fifth of the price. Getting a set of pin tweezers like this is not required but will make things much easier.

I would strongly advise you do NOT practice on your own door locks. Pick up a cheap lock from a hardware store (one that does not say "kwikset smartkey" and does not have this little hole beside the keyway) and practice on that instead, because you are almost 100% guaranteed to fuck up your first attempt. Repinning a lock cylinder is not rocket science but it's no walk in the park either - even after years of practice and hundreds of rekeys I'll still occasionally slip up and dump my driver pins or some other stupid mistake. And if something gets fucked up in a way you don't even understand, you'll most likely need to pick and shim the cylinder to get it apart again, and unless you already know what "pick and shim the cylinder" means, you'll probably need an actual locksmith to fix it. You do not want that headache on the lock you use on your front door, and a random deadbolt lock to practice on is literally less than 20 bucks.