Yamaha MG102C mixer or something similar, I got mine on a scratch and dent sale for $80. 8 channels. A small mixer is a great place to start.
It's the hub of the practice station, with a vocal mike, drum machine, cd player, tape deck, ipod, guitar, computer and bass hooked up to headphones. 98% with headphones, but I can also run the whole mix out to a power amp and monitors and PA speakers. I use an old Alesis microverb for effects.
Bass guitars don't put out a lot of signal in many cases, so a Di box may be in order. I use a MXR M-80 bass di +. Look for one used in the TB classifieds. I use mine for everything. Preamp, boost, some distortion, it's been around forever, while others have come and gone.
Having a DI box in your kit lets you hook into PA systems when you go play somewhere and don't have an amp. It might save your butt some night when your amp dies.
I've had headphone amps like the Bassman from Schultz, but the mixer has been a huge improvement and much more practical solution.
The whole practice station sits in a shelving unit at chest height and takes up about 6 square feet in the corner of the room, so I can stand up to practice, or pull up a chair. I added a little keyboard shelf to hold music, and also use magnets to pin up papers.
On the other hand, since you mentioned a usb port and you might have ideas for integrating your computer for recording, practice, and playback, a simple usb interface with a headphone out might suit you. Also, some multi effects units and loopers have headphone and usb outs. Depends on how portable you want to be. And being chained to your computer can be less than productive. I try to keep mine ten feet away.
If you have a mac, check out garageband and irealB.
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