Classy escort service - they charge several hundred per hour, worker seen should take care of any need you have, you are likely to be heavily screened (employment verification, credit check) before you get an apt. The worker is going to demand 100% protection (if she is worth the price tag she is charging).
The worker will typically be avg citizen who happens to like sex and could use some money. Should be very asthetically pleasing, but for those who may prefer something else, keep looking, its probably there.
Legit escort services - technically, any "escort service" is legal, but its a technicality. The tech part is that you are being paid for your time, and your time only. What else happens between two consenting adults is their business. If they are getting busted by the cops, its usually not a big enough technicality to hold. On the other hand, the only way they get most prostitution charges to stick is by tacking on something else - drugs work quite well, but anything will help the prostitution charge stick.
EDIT: Just to be clear, any multi hundred per hour worker is going to be safer than the one night stand from the bar. Not only will she NOT be looking for anything more than sex, she wont be calling your phone for your wife to pick up, she is also far more likely to demand condom use, many std screen before they see a client (themselves and the client), and virtually all take themselves to the doctor for screening and bc regularly.
Do all of them? No. Do your homework.
as others have said, its not that they are really viewed as classy, but its a way to seperate them and their services from the strung out worker danging on the street pole, or the worker being pimped out of a backseat.
There are agencies, but virtually none of them will be operating they way a pimp would, and workers on this level are free to work for themselves as well.