Over the last 30 years homebrewers have used many methods to create beer at home. The old homebrew was the kit and kilo, that is a prehopped can of goo and a kilo of some sort of sugar, whether it be table (sucrose), maltose or dextrose. This is still a popular method but is limited to the kit, certainly you can add extra hops, use a better yeast but the limitations are still there.

The “gold standard” really has been all grain. By using all grain of a single or multiple types that you freshly crack yourself, mash (soak) at a temperature or temperatures to create precisely the malt profile you want you create your own wort. But this can be expensive and certainly not something you want to do on your stovetop.

A method that has always been popular in USA is a hybrid extract/specialty grain method. For this all you need is a large pot something like this is ideal as it keeps you out of the kitchen https://mashematics.net/wp/shop/#!/DigiBoil/p/722599662

You then steep specialty grains in a grain bag for 30 minutes, add malt extract bring to the boil and add hops according to schedule. You may choose to do a full boil which will add efficiency to the hop bitterness extraction but if you do this you will need a way to quickly cool the wort (immersion chiller, counterflow chiller or plate chiller). You may choose to cube in which case you will have the equal of the Fresh Wort kits sold by some retailers but at a lower price though I personally think that fast cooling greatly improves your beer.

Alternatively you you use a smaller boil volume and simply add cold (icy cold) water to volume. This will still create cold break and is unlikely to create any sanitary problems so long as you promptly pitch yeast. You can buy an OK 15 litre pot from IKEA for $45

Here are some suggestions: https://mashematics.net/wp/shop/#!/Beer-Ingredient-collections-Basic-Brewing/c/41814070