Hey python8! welcome to the forums!
Honestly, I thing you're going to have a hard time making decent recipe for $25 or less without going all grain. While I understand wanting to make cheap beer that still tastes like beer, there is only so cheap you can get before making sacrifices. I suggest you raise your price-per brew $30. If you're making a 5 gal batch (at least 50 12oz bottles), that raises the price-per-bottle from $0.50 to $0.60... which means your beer is still dirt-cheap.
At the price you mentioned for LME (Liquid Malt Extract), this leaves you with:
- 6.6 lbs of LME - $23.00
- 2 oz hops - $4 to $6
- Dry yeast - $1.50 to $3
This should put you into the $28.50 to $32 range.
If you're dead set on trying to stay below $25, here are some things you might look into:
- DME (Dried Malt Extract). I have no experience with this personally, but I believe that for the same targrt gravity, you need less DME than LME. Can anyone confirm/deny this?
- Buying in bulk. This is going to cost more up front, but will drop your cost per batch.
- Going all-grain. Normally this requires a bunch of gear, but the BIAB (Brew In A Bag) system is incredibly cheap to do.
- Make smaller batches. While probably not dropping the price-per-beer, doing a 1 gallon batch or a 2.5 gallon batch will be cheaper per batch, even if it's not cheaper per beer.
- Brew low-gravity beers. You're gonna have a hard time making a 8%abv IPA for less than $30, let alone $25. But you might be able to get a session ale (like, a 4% English brown ale) for around $25.
- Use table sugar as a fermentable. BE CAREFUL WITH THIS ONE. While it will save you money, this is a very easy way to make your beer taste bad. A small amount might be acceptable, but too much will affect the flavor. Also, purists and beer snobs (probably the vast majority of people on this board) will judge you if you do this.
Good luck with the brewing!