Need some help regarding mixers and interfaces

This topic has been big to swallow for a beginner like me.
I'm trying to start a home recording studio like most out there but there's just this one thing that is an obstacle yet
to overcome. This is where i need your help.

First i'll list down the number of instruments/inputs i'll be having (soon)
Vocals: 1 condenser mic
Electric guitar: 1/4 jack
Digital Piano: 1/4 by adapter?

OR

Vocals: 1 condenser mic
Guitar : 1 dynamic mic x2 (max)

So at any point of time i would need 3 to only 4 inputs.

Now here's the problem. I want a mixer(with built-in interface) so that i can record and play live as a band and also
mix with onboard faders and knobs. Upon days of researching and confusion i've learnt that most non-expensive mixers only has a stereo output which would mean that i cannot record all 3-4 instruments together at once into separate tracks into my DAW. Also i'm not use if i use a 4 input interface, i can only use to record it but i can't just play live if i do not want to record?

Shed some light. Thanks!

If you are using only 3-4 even possibly up to 6 inputs upgrade ability consider the zoom h6.

You want faders and knobs then go for zoom r24

http://www.citymusic.com.sg/webshaper/store/viewCat.asp?catID=40

At about a difference of $70-$80 it's 2 channels and portability. Though, both are portable!

Personally using the discontinued version zoom r16 and my experience with zoom's earlier recorders they're not built like a tank (solid metal etc) but they do deliver it's purpose cost effectively as long as you're not using in the middle of a moshpit or wall of death