First off, the quality of sound in the headphones will not be even close to what you will hear in the control room. Headphone use is designed for you to hear the other players so that you will all play in time together. Do not be concerned about how the tones sound in the phones. If you hear any weirdness in the control room at playback, then mention it to the engineer. You do need to hear yourself and others.
Make sure you have the mix that you want. It can help you perform better and maybe even inspire you to greater creativity. For guitarists, if you are in the same room as your amp try an open ear phone. This will let you hear more of you amp acoustically.
Bass players, use a closed phone with good bass response so you can hear the bass better. Drummers, the same as bass. Closed headphones will help you hear the bass and drums better and will keep the click from bleeding into the mics.
Vocalists, the use of headphones is very tricky for you. Singers usually sing sharp or flat when using both ear pads. To help remedy this situation take one side of the ear pads off. But be careful, you don’t want the sound from the headphones going into the vocal mic. So, watch your levels.
One last item of note, most studios today only have 2 to 3 mixes for headphones so you may need to share a mix another player. Drums and bass go together well, keys and guitars go together well also. If you are doing vocals live, try to keep them on their own mix.
What is your favorite headphone monitoring tip?