Brewing is a real joy for me, and I wish I had time to do it right now. This is a pretty cromulent price for a basic 1 gallon starter kit, and has everything you’d need (ostensibly) to make something reasonably beerlike. The instructions are pretty good, and will certainly get you where you need to be.
You’re going to hate bottling, almost assuredly, with the included stuff. A bottling bucket and wand definitely make it less painful, but that’s money you may not want to put in to this hobby until you know you like it.
When it’s in the active fermentation stage, it’s good to keep the liquid temperature around 65-70F if possible. Since those little yeasties generate their own heat, it’s always going to be warmer in the fermenter than it is in the room. Basements work pretty well, usually.
The upside is that even if your first attempt turns out badly, you’ve got the basic stuff to try again. Grain, hops, and yeast are inexpensive, especially if you’re only doing a gallon at a time. Lots of vendors online, and you can get more brewing info (recipes, advice, whatever) than you’ll ever need at homebrewtalk.com or the brewing subreddit.
Shout at me if you have questions, I love to talk brewing!