need help with basic recording setup onto computer
 

What I would like to do:
Record tracks from electric bass, double bass, keyboard, vocals
Modify each track and mix down
(I would also like to learn how to record live several instruments onto computer and be able to adjust levels but not sure if this is possible with what I have.)

Here's the equipment I have:
Behringer Xenyx 802 mixer
Behringer UCA222 USB soundcard
Garageband/Logic
Headphones
Yamaha digital keyboard has a usb out put as well as a phones/output
bass instruments

What's the cleanest way to do this with the equipment that I have? Is an active DI box necessary?
Where should monitor headphones be coming from and is it possible to adjust monitor headphones to best suit each individual?
Thanks in advance for taking the time to help me as I begin to learn recording methods!

You could run your bass in the mixer, then from the mixer to the sound card which will allow you to record in the computer. I'd use Logic as the DAW of choice. With most DAW you can record multiple instruments at the same time or record one instrument, then go back and record another while playing the previous track you recorded. If you're going to record multiple instruments at the same time then you're probably gonna need another sound card with multi inputs.

powered mixer vs. DI box?
 

Thanks. I was wondering if the mixer, because it has its own power source, does the job of a DI box? Would one of these be redundant or significantly improve the signal? Thanks again.

it should mix it to a proper level but the DI should not hurt it. You will need a microphone for double bass (probably a compressor Mic) and a vocal microphone, although a compressor could work for that too

I second that. Or a clip on mic for the double bass. Either will do the job but the compressor mic advice would probably serve you better.

I just ordered the MXL 990/991 package off MF for $70

MXL makes great compressor mics that don't hurt the pockets. AKG makes a few also.