A friend of mine who DJs has gone through the process of learning how to properly work music for competitions. The things he's told me about are:
* Music licensing. In the U.S., you need all three of ASCAP, BMI, and SESAC. Sometimes the venue already has licenses (e.g., a studio), but if you are doing comps, you are going to be working in a lot of venues like hotels and civic centers which will not have licenses, so you will need your own.
* Appropriate music. You need to make sure you have music with the proper tempo ranges for the dances involved, and that means getting familiar with the NDCA and USA Dance standards for American style, and ISTD for International style. You need to edit off any non-strict-tempo beginnings; the music should come in with the proper beat and tempo right away. Ideally, you want enough music so that it is not necessary to repeat a selection during a session, although you can get away with a few repeats. Pay particular attention to your music selection for Paso Doble; you absolutely must have a version of España Cañí.
* Decent sound system. Goes without saying. In particular, an equalizer helps with achieving a good sound in different venues. My friend has also invested a lot of money into lighting, which isn't essential, but it can significantly enhance the mood versus the typically flat lighting at most comp venues. Whatever you get, you want to make sure that it is rugged and not too heavy, since you are going to be moving it a lot.
* You want a music system that will allow you to quickly find selections from different genres. I think most DJs typically build a playlist for each session, but it's fairly common to change the order of heats during sessions for various reasons, so you don't want to be stuck in a canned playlist. You also need to make sure that you can easily import dancer-supplied music for solos.
* If you are also going to be the MC for the comp, you want a decent mic and you need to work on your public speaking voice.
* Make sure you have an electrical outlet tester. You can get a simple type from one of the big-box stores that typically has two yellow lights and one red light. You plug it in and if the two yellow lights come on and the red one doesn't, the outlet is good. I've found in the past that a lot of public venues have improperly wired outlets. Be safe.