Hi! Sounds like a great plant! I imagine it will take some time to repot - probably has a mass of long entangled roots - so leave yourself some time for doing this. I have found the "jet" setting on the hose sprayer attachments is helpful for loosening and getting out old media, and detangling roots. Cut away any dead roots. Choice of media varies, but it should retain some moisture while still draining well. I use a mix of fine and medium fir bark for orchids, with added perlite and styro pnuts (if you use styro pnuts stay away from the pink ones, as well as the biodegradable type). Coconut husk chips with perlite (and pnuts if you choose) also should work well.
If you choose to divide the plant each division should consist of at least 3 older pbulbs with at least one new growth - but larger divisions are better. The old "brown" leafless pbulbs can be removed if you want. They can be propagated if that's something you want to try, tho plants propagated will be a few years before they are bloom sized.
How big is your cym now? Would love to see a pic if you care to share