Car keeps stalling out and dropping idle

I just bought my 2005 rx8 a month ago and it has just started having issues. I replaced the battery because it was bad thing it would fix the problem. The issue seems to be after I drive for a little while. When I get to a red light or have to stop it drops idle and acts like it wants to choke out. As I was pulling into work this morning it completely shut off on me and wouldn't start back up. This same issue happened two days ago and I got a jump from some one and it started right up. With me putting a new battery in yesterday I'm starting to think that's not the problem. My car has a rough idle, it kinda takes a second to turn over when I start and it sometimes feels like I'm loosing compression. I'm at a loss right now this is the first one I have owned and I have always wanted on, now I'm stuck trying to figure out this new type of engine to me. I need all the help I can get