most of those recorders allow for external mic inputs so if needed, you can use a good vocal mic for the singer, then have specialized mics for the instruments.
If you want a professional sounding recording then the vocals and the instruments need to be on separate tracks. Instruments are generally louder than vocals and heavy bass or anything that causes the diaphragm of the mic to flex heavily, it will prevent the minute articulations from happening thus if you record everything at once with the same mic, you will get issues such as vocal detail being lost when ever a bass heavy or loud instrument is played.
the H2n seems pretty good http://www.samsontech.com/zoom/products/handheld-audio-recorders/h2n/
offers a decent level of control over the stereo field
wanted to add, it is very easy to use these mics with the camera, if the mic allows for real time monitoring then you can connect the audio out, to the line in on the camera then record (the camera will save in a more lossy format but the lossy track is still good to have because you can use it later to sync the higher quality audio track with the low quality camera recorded audio, then the high quality audio will be in sync with the video without the need or the time consuming process of using a slate this process allows for greater accuracy than with the slate since the slate method can cause the audio to be out of sync by as much as 40ms (though not noticeable unless someone examines the video very closely for a frame of video that does not match with the audio directly under it, eg the audio of a firecracker exploding happening 1 frame before the video (not really noticeable in a 24-30FPS video)