Couple of things after glancing through the instructions:
The 2.5 gallons you'll actually be boiling is probably doable on a stovetop. I've never done more than a 1 gallon on the stove though. If you have a turkey fryer, you'll be able to rip through it in no time up to close to 6.5 gallons. I've since switched to a dedicated burner but that turkey fryer did way more beer than turkey.
Instead of water for the airlock, I use vodka. Won't evaporate. Any cheap shit will do.
I like to do the secondary fermentation personally. The manual says optional, I'm not entirely certain I agree.
When I first started brewing, I only used distilled water. After some thinking about it, went with straight tap water figuring it'll give my beer a more unique flavor. Harder and softer water are preferable for some styles though. If you get into doing this, I'd test your water.
The only other thing I'd warn you about is the priming sugar for bottling. At least for me, it's the most frustrating part of the process. You won't know exactly how much sugar to use because you don't know exactly what the yeast is up to at that point. I've had some a little flat and others were bottle rockets. For a kit, I'd hope the numbers are dialed in for you. I'll admit I've never gone that route-- I've only ever done all-grain brews.
Last, it's a prerequisite to have a few beers while you brew. That and if you enjoy it, kegging is the way to go.
Good luck!