Assuming you have already decided on media - of which there are lots of choices......
Do not oversize your new pot - just large enough to comfortably fit your roots in.
Many of us like to use clear pots in order to more easily view what is going on inside (added "comfort" level) - they seem to potentially contain the roots a little better too, or maybe just my imagination? You can always put your clear pot into another pot for show when blooming as well.
Trim off all mush, black, dried, etc. roots - keep all tan/green/gray thick firm ones (of course).
You might want to think about soaking the roots and media for a spell before repotting in order to make the roots a little more nimble and easier to turn/bend and place into their new (or cleaned up) pot.
I like to put a layer of styrofoam peanuts in the bottom of the pot for additional air circulation and drainage. Be careful not to use the kind that turn to goo when wet.
If you are using bark I'd be sure and soak for at least 24-48 hours. Some poor quality bark will also require soak/watering for the first few months in order for the bark to start retaining water sufficiently.
Take a picture of the before and after and post if you can! Love to admire your work.
