If you already have a vocal mic that you use for PA, Behringer's dinky Xenyx 302USB mini-mixer would do the job - I've got a couple...
The mic input has a combined XLR/6.3mm jack input (with phantom!), which is paralleled with a 3.5mm jack next to the headphone socket - so you can use a headset with it. It has a peak (clip) LED, low and high EQ and a pan pot.
The device is USB bus-powered, but comes with a USB wall wart (really a USB charger plug) so it can be used as an analogue standalone mixer - handy on stage if you're short of tie lines, as you can send both a microphone and line-level source up one line - particularly useful for keyboard players.
It's comparable in price to a basic active DI, but will do a lot more including EQ - just remember the stereo RCA/Phono output is unbalanced line level, not balanced mic level.
The stereo line input can be switched between RCA/Phono line in and the computer output when it it plugged into the USB port - it replaces the sound card. Better still, it can also be switched between headphones and main output, making it useful for just the overdubbing you wish to do.
There's also a '2 track' input with no gain controls - this, too, is switchable between headphones and main output.
Somebody really though this thing through - though someone will always find something they wished it did, or wished it didn't... you can't please everybody!