Just do it ...
If you don't shift a-lot-or-ever because of the flat terrrain then you may want to go with a Single Speed configuration ...
If your bike has a Freewheel, then you can replace it with a single Cog, BMX Freewheel (choose
ACS ... if your bike shop doesn't carry them then get one at DANSCOMP.COM or via eBay) ... BUT, you will probably need to have the rear wheel re-dished.
If you opt for a Single Speed, then decide what gear combination you are currently using the most ... and then, figure out how many teeth you want your Single Speed Freewheel to have.
The most teeth on an off-the-shelf Single Speed Freewheel is 23 ... but, it's a bit expensive compared to most other BMX Freewheels ... the next largest size has 22t and will cost about 1/4th as much. Most people seem to choose a 16t as a "safe" intermediate size.
BMX Freewheels come with either 1/8" or 3/32" wide teeth ... choose the latter because it is the standard ROAD size and will allow you to use standard ROAD chains.
1/8" is common on TRACK bikes, on some BMX bikes, presumably on some Cruisers, etc.
Even if you don't go the Single Speed route, you probably don't need more than one chainring on the front ... so, you won't need the front derailleur.
If you opt to keep multiple gears on the back end, then you can continue to use the rear derailleur you have ...
If you want to change it, then you need to choose the brand which matches the shifters you have ... if you have Shimano shifters, then you generally need a Shimano rear derailleur. Almost ANY Shimano Road rear derailleur will work for you from the mid-90s through to the recent 10-speed types. A
used 105 rear derailleur (5500 or later) will work.
If you have SRAM shifters, then (IMO) it is probably worth getting the least expensive Shimano shifters + a Shimano Deore-or-better rear derailleur OR go the Single Speed route.
BTW. MOST
MicroShift rear derailleurs are Shimano 8-to-10-speed compatible. I reckon that they are about
105 quality; so, if you want NEW-instead-of-USED rear derailleur, then look at theirs (at least one of Nashbar's ROAD rear derailleurs is a Microshift).