Nice starter set you have there. You'll be hooked in no time at all. After that first batch you'll be like, damn my beer tastes so good.
Don't stress the process too much. I would say the most important thing is really just to have everything clean and sanitized. Especially your bottles.
I have been brewing in Jamaica since Jan and I don't have a cooling system yet and my beer does just fine.
It usually ferments at about 85F, which is really high, (first couple of days is probably even higher than that) I try keep it in the darkest coolest part of the house, which is difficult in Jamaica. (So far I've done an Amber Ale, Peanut Butter Porter, Chocolate Milk Stout, American Cream Ale and again an Amber Ale. Got the Peanut Butter Porter, Gluten Free Ale, Peanut Butter Brown on order. Gonna brew those soon.
I've done mostly ales and they seem to do just fine with a higher temp. I am going to get a cooling system in the near future as I want to start trying other styles. Got a Belgian Saison and Kolsch on order. So keen to see how that does in the temp controlled environment.
My first batch was an amber ale, just the basic homebrew kit with recipe from Northern Brewer. Followed it as best I could. Didn't have a wort chiller, hydrometer or anything. Didn't know what temp I pitched the yeast at, just let it cool down...and the beer turned out great. Was just lucky I guess.
Since then I've bought a bunch of extra stuff. Such a great thing to get into. Really addictive.
Have fun