I'll be glad to answer that for you.
Normal coin operated pool table sizes are either 3-1/2'x 7' or 4'X8'. These usually have a single piece of 3/4" slate in them and their total weight is between 400- 500 lbs.
There are also drop-pocket tables, non-coin operated tables that are usually 4-1/2'X9" in size , and these usually have a 3 piece slate installed. Keep in mind that the above sizes are the sizes of the slates, and you should add an additional 6" to the width and length of each table to measure total width and length.
I would not even consider buying a pool table such as those advertised at Sam's Club or other retail outlets because the greatest majority of those incorporate a bed that is made of plywood, and is rarely able to be leveled properly.
To determine the proper size for your room, you should allow at least 3' all the way around the table for the players and stick movement. So any room you are going to put it in should measure approximately 11'X 15' or greater.
A large table with a 3 piece slate is the easiest to maintain, but the heaviest and most difficult and expensive to recover.
For your price range, I would recommend either a 3-1/2'x7' or 4'x8' table. This is for a USED table though. A new one will cost you hundreds or thousands more. Still, you should be able to get a decent used table for that amount. The coin-operation can be bypassed so that it operates on Free Play. At the same time though, the coin-operation will allow you to save some money for future needs.
As for what brand name(s) you should look at, as far as I'm concerned there are only two.
Valley or Dynamo. They are the two premier names in coin-operated pool tables, and I wouldn't consider any other name. Not long ago the two companies merged into what is now Valley/Dynamo Billiards.
Please feel free to PM me for any further details or questions.