The "audience mic" is a common channel on the mixer for a live event, especially comedy and shows with crowd interaction.
You definitely want a "condenser" microphone, first off. Most of the mics you put on a stand for spoken word and even a lot of singing are "dynamic". The difference is primarily in how the microphone's diaphragm turns vibrations into sound, and the short of it is that condensers are more sensitive to minute vibrations, which is desirable in a wide array of situations, but they require a power source in order to produce their signal (this is typically provided along the signal wires themselves by the mixing board, which is called "phantom power"). They're also more expensive; you can get an excellent dynamic microphone between $100 and $200, while the really nice condensers (relatively speaking) can top $1000. You don't need that kind of mic for what you're doing; the best I'd bother with for an audience mic is a $500 AT4050 multi-pattern (and only because the mic would be versatile enough that I'd have it sitting around in my mic trunk to use for any gig that got up on stage).
Second, the pickup pattern of the microphone is important. There are two patterns you can consider for an audience mic; a "cardioid" pattern or an "omni" pattern (that AT4050 I mentioned allows you to choose either one). There are also "figure 8" and "supercardioid" patterns; they're more suited to specific situations, and not a great fit for yours (though if you got a figure-8 and a cardioid you could experiment with a mid-side configuration; that's probably more than you need).
A cardioid mic is pretty simple; it's most sensitive to a sound source that it's pointed directly at, and it's least sensitive to a sound source directly behind it, with all other possible directions around the grill of the mic generally falling into a gradient between the two. On the plus side, a cardioid can be aimed away from any speaker cabinets on-stage, placing them in the mic's deaf spot, and so it will reject bleed-over and feedback from them. The downside is that all "directional" mics including cardioids are subject to the "proximity effect"; the closer a source is to the microphone, the bassier the sound gets, and the reverse is true as you back away. This may require you to find your EQ balance for the crowd mic while the show is underway, depending on who's sitting close to the audience mic and how loud they're laughing or shouting.
An omnidirectional microphone is even simpler; at every point around it, no matter how it's positioned, it's equally sensitive to sound. This means that an omni is pretty hard to point in the wrong place; you just put it somewhere and it will do its job. Omnis also have no proximity effect; someone closer to the mic will sound louder, but not bassier. The downside is that because it has no "deaf spot" in its pattern, you have to be careful where you put an omni in the room; an omni too close to a speaker will bleed over, feed back, etc. Now, you aren't going to want to route any of the audience mic's signal to the mains, so feedback shouldn't be an issue; it should only go into your recording feed (usually either a matrix or a pair of auxes), but you still have to control bleedover because it can induce a delay effect into your recording mix (you'll be recording the comedian through his mic, through the audience mic, and through his mic, out the speakers and into the audience mic, all at slightly different times).
Usually, isolation of an omni is done simply by keeping its gain low; with the signal level low, bleed-over will be low. Audience laughter is usually loud enough that you don't want a lot of gain on the audience mic anyway. You will have trouble hearing one guy in a crowd shout out something to the guy on stage; even the best setups don't close-mic everybody in the audience. It's generally considered an acceptable tradeoff, given that what the audience mic normally gives you is the laugh track to the routine, which is a cue to the listener that they should be laughing as well.