I started with a $140 kit and currently only use a few items from it.
My current setup is a mismatch of items I've put together but if I was starting from scratch, I would probably buy
Clawhammer's starter home brewing system . It's fully upgradeable to having a electric heating element and controller, a pump, a recirculation kit and a plate chiller, but you can use it as-is, on the stove top.
You would still need some other items, like a hydrometer and vial, one or more buckets for fermenting and bottling, plastic spigots, an auto-siphon and tubing.
You could also do something like the
Brewzilla or the
Anvil Foundry , which are less expensive than the Clawhammer system but less modifiable and repairable, if something malfunctions.
The most important thing I've learned is that temperature control during fermentation is the most important part of home brewing. I invested in a 5 cubic foot chest freezer and a fermentation heating pad, along with a digital temperature controller, for this purpose. I also purchased a stainless steel fermenter with a thermowell, which allows me to place the temperature probe in the middle of the wort, for an accurate fermentation temperature reading. I have a stout fermenting right now and this system keeps the temp within 1 degree F of where I set it. I think you can mitigate this issue by using yeasts with higher temperature ranges but for me, that is somewhat limiting in what I can use.
Watch some Youtube videos on electric BIAB (Brew in a Bag) systems. The three I mentioned fall into this category and the basic process is the same for all of them.