I am looking to record some music that my brother and I wrote. It is acoustic guitar, a single drum, and auxiliary percussion. We will also be playing it live. Is there such thing as a digital/analog mixer that we could use live and for recording? Not looking to spend a TON of money
use live how? if you need your own mixer, you probably need your own PA as well, not to mention mics for each instrument. This is becoming a ton of money. You can get dirt cheap mixers and dirt cheap recording interfaces. Units that do both like the Zoom R16 might be within your price range but don't amplify.
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This is literally all you need. If the music is good. This is assuming you have access to a PA for free.
This is very low budget but you could make it work.
As long as you don't intend on doing any post-production work on the individual tracks you can get mixers that have a stereo USB out (Behringer makes some which are decent value for money). If you pick the right mics you could do all that with two mics.

The cheapest effective combination I can think of would be a Behringer Xenyx Q1002USB (smallest one with two mic inputs) and a pair of Behringer C2 microphones. That should total $200-$250 and is the absolute cheapest solution I can come up with.

Also "unofficiallyme2" new members are unable to post links right away as a spambot-deterrent. It's usually better just to post names of products, especially to keep threads usable in search (sometimes a sweep gets done where all links become forbidden).