I didn't suggest the 1 gallon kit.
I did say starting with stovetop extract is the way to go for almost anyone new. A 'standard' batch of homebrew is 5 gallons, and this is based on the fermenter size where it used to be based on the 5-6 gallon acid carboy that labs used. The OG homebrewers had to repurpose whatever they could find, and the 6 gallon carboy made a 5 gallon batch which conveniently is easy to bottle and/or fits neatly into the 5 gallon Coke/Pepsi soda kegs that were being discontinued and sold cheaply. 25 years later there so much new tech and hardware you can make pretty much any sized batch you want, just be aware that 5 gallons is still the standard size and then pretty much goes up in increments of 5.6
The Boil
On the stove top you'll generally boil about 2 gallons of wort, this is based entirely on the power of your stove and the size of your pot, but you do need to bring it to a boil, uncovered, for 60 minutes. Then you need to cool it down as fast as you can. For first timers, this is generally done by placing the boil kettle into your sink full of water and using a water bath to cool it down 70F or lower. Just keep changing the water out, then add ice to your water bath, this is time consuming. If you get the bug and love it, then spend a little coin on an immersion chiller. Once you remove the pot from heat, you can put the lid on.
Once it's cool, you'll dump the wort into your fermenter that has 2.5-3 of chilled water in it. There's some ways to cheat the cooling process, if you have the 2.5 gallon jugs of spring water from the store, put it in the fridge overnight, then when the wort hits 85F or so, you can put the chilled water into the fermenter, and then pour the wort into it. Never put hot wort into a fermenter first, always cool. The volume and temp differences will allow you to hit your 'pitching' temp when you add yeast.
Follow the kit instructions on when to add X to the wort. And as it comes to a boil, watch it. You want empty space in the kettle to avoid a boil over, this is the most tricky part of brewing indoors, a boil over leaves a mess and a very unhappy wife.
Cleaning and Sanitizing
This is part of the science that cannot be over looked. Clean everything with PBW as this dissolves organic material, get a home depot bucket and then make up your sanitizer. Your kit should come with both so follow the directions. Once the boil is done, anything that touches the beer has to be cleaned and sanitized. Carboy, bottling bucket, tubing, spoons etc.... Wort is nothing more than sugar water and all wild bacteria and yeast is looking for an easy meal, don't give it to them as has the chance to spoil your beer.
The Fermentation
This is a critical point, 1, you can't add the yeast until the wort is below 70F (for most styles, there are always exceptions). You can never add yeast to boiling wort, it's a living organism and you'll kill it. And that it is living, it has a happy medium written on the package for where you want to keep temps stable, generally between 60 and 70. Now is a fantastic time to learn because you're not trying to ferment in summer when the heat is a real issue and requires other work arounds. Generally, give it 2 weeks. Ignore anything that talks about a secondary fermenter, it's not needed for basic beers.
Packaging
Once the wort is done around 2 weeks, you're ready to bottle. Your kit should have a bottling bucket where you'll add priming sugar to it, then siphon your wort in, then bottle and cap. Lots of youtube videos on this. In general, you don't want to splash the beer into the bucket, you want to slowly siphon it over, else you oxidize the beer and you ruined it. Then let the bottle sit warm for 2 weeks while the yeast eats the priming sugar, farts CO2 and carbonates your beer. During carbnoation the yeast will scrub and consume any oxygen it picked up during bottling.
Chill and Enjoy, by decanting the bottled beer into a glass, you don't want the yeast sludge on the bottom as it'll give you wicked farts.
As you grow into the hobby your gear will change greatly and you'll learn different techniques, buy different equipment etc... It's possible to make great beer with basic equipment, or spend tens of thousands on a homebrew rig.
