First, if you have little or no experience, don't expect to fight before 2 years of consistent training. Any trainer that wants you to fight professionally before that doesn't know what they're doing. Also be prepared for 2 training sessions a day, 6 days a week. That's what it will take. You will get hurt. Your real job will suffer. You won't have a social life. You won't make much money. If that sounds good, read on.
As far as facilities, the only absolute musts are a cage, mits and thai pads, and sparring partners. You can't train to fight properly if there is no cage you can practice sparring in. There is a big difference fighting in a cage, versus open mat space. Strength and conditioning equipment is nice to have, but a good trainer will be able to condition you without it. The bottom line, you should be much more concerned with the trainer than the facilities.
Picking a good trainer is tough. The best way to judge is to look at their students. Do they have any professional fighters? Are their fighters successful? Has the trainer fought professionally? Ask how many fights the trainer has cornered, if he knows how to be a cut man, etc.
Starting out is about getting conditioned and picking up the basics. You'll need to drop your bodyfat to at least 8%. That means dieting and lots of intense workouts. You'll learn how to move around properly without going off balance. Basic striking, take downs, and grappling will be the other bulk of the training. This will be followed by basic defense. It's a slow process. You need to be able to fight effectively, at weight, with enough gas in the tank to go 3-5 rounds. Minimum 2 years before you're ready.