It's really up to you how you get the data back to the game. When you use classes like URLLoader you can send variables (via GET or POST) to the server to authenticate and route your request. At that point your PHP script is responsible for reading the request and responding with the information however you like it.
For your first game I would recommend you stick with very well known structures like XML or JSON for responses from your PHP scripts.
For example, if you use JSON, you first set up your request in AS3 telling it that you will receive plain text back (not binary or URL encoded variables). Your PHP script receives the request, performs the necessary operations (on the database, etc) to get the information you need. It is then responsible for structuring it back to what Flash is waiting for (JSON) and as you probably know PHP has JSON encoding built in (http://php.net/JSON). After you craft your response and print it out, AS3 will consider that a response. Then on the AS3 side you decode that JSON and use the information as needed.
Eventually in the future when your game scale gets larger you can start making web services that handle more efficient binary formats like AMF. While you can do it with standard POSTs it's not always even worth it performance wise. Also you'll go from HTTP requests to direct socket requests. If your game is of a standard type you may even use RESTful based web services so look into those if you're not familiar.
Yes, you'll need a host, however I can't recommend one because I have no idea what you're building. If you're planning on building a MMO then no web host is really going to give you an inexpensive cluster hosted account for that scale of a game. If it's just keeping track of leader boards and user accounts then I often use hosts that can scale from tiny/cheap to dedicated using my own hardware, like site5.com.