A stereo handheld recorder may be sufficient if you want to get a useful warts 'n' all recording of one of your band's gigs, but the balance may not be all that brilliant and you'll likely have to contend with audience noise and other peripheral clatter near the stereo microphone.
It's probably far better if all the instruments (via mic or DI) are going through the mixing desk. This will allow you to record the individual channels to a multitrack recorder for mixing later, giving you a cleaner sound, a better balance and the chance to create a pro-sounding 'live album' that you can sell.
Cymatic Audio's LR16 Live Recorder will let you do just that, offering 16-track recording direct to USB with audio files that you can then transfer to a DAW for mixing.
Extremely easy to operate, the LR16 simply connects into a mixing desk's channel insert points via TRS jacks, taps off some of the signal without affecting the front of house mix, and continuously records 16 wav files at 16/24-bit, 44.1- 48kHz. All you need to do is hit the record button and it will capture a whole multitracked gig to a connected USB 2.0 hard drive.
What's more, it also doubles as a USB audio interface, so you can use it to record to a computer or an iPad.
If you want multitrack recordings of your gigs and rehearsals, the light and compact LR16, together with a pair of eight-way cable looms and a USB drive, makes a portable and cost-effective package for the task.