One approach would be a lav on each person.
No matter how they lean in or out, they would be on-mic.
Otherwise about any desk mic will work, one for each person.
There are lots of good mixers, but under these conditions you want an audio OPERATOR to mix this live as you shoot.
Just having all four mics UP all the time (even split into two channels)
can be a big reverb, cross-leakage, and background noise mess.
A good operator can quickly run the gains on each mic (balanced levels) and take the folks not talking out of the mix (less cross-leakage).
If you want a very versatile mixer for the best price you'll ever find, look here:
http://www.musiciansfriend.com/srs7/g=home/search/detail/base_id/54496
The Behringer MXB1002 can mix 5 microphones (!) and/or 4 STEREO line sources, and, if you need it on-location, can operate on three 9v batteries (including phantom power for the mics). It costs... $100. (I own one and its amazing for the money).