"mixer"
No.

You want an interface. Alesis MultiMix's and such are useless and only record a stereo mixdown. So you get landed with a fixed track that you can't tweak parts of.

What you want is a multiple input interface. With preamps. Or search hard and you might find a mixer that actually records more than 2 tracks but this is unlikely and excessive. Like buying a house to use the bathroom.

Ok thanks, can you recommend me an interface?

Thanks.

Interfaces are best treated like shoes...
Find your own - I can tell you what shop to go to but not what pair or size or colour to buy.

Also, there's been plenty of people asked this question beforehand, with a slew of different needs, mainly in "Home & Project Studios"/"Budget Gear".
(You can try the search function, but it's finicky)

You want one preamp per mic you want to use concurrently. You may want phantom power for condenser mics or active DI boxes (for guitars).
You want one Hi-z input for each simultaneous guitar (bypassing the need for a DI box).
You want one line input (or stereo pair) according to the number of keyboards/synths/drum machines you want to connect simultaneously.

For anything over 2 inputs, you'll want to avoid USB if possible.

I could say "Presonus FP10" which is a pretty good starting point but might be too expensive. Sometimes you gotta make compromises.

Ok I'll consider it. What do you think about the Tascam US 1641?

Thanks!

Would two SM57's be good as overheads?

If not which mics do you recommend? (I'm kind of on a budget)

Thanks

Overheads are as good as you can make em ;)

I can get "acceptable" sound from a single mic that ain't as good as a SM57. Just find a place that they work and stick em there. No not there! To the left a little...

You should be able to get something good with them, and with the right placement, it'll be even better.