I had a chance to chat with few BMW instructors/test drivers at various BMW events. Their common opinion is that unless you're going to track it, M3 is too much of a car. M340 is more comfortable and both of them are equally capable of reaching go-to-jail speeds on public roads.
To be honest, $90k/yr probably wouldn't let you to comfortably own either if these BMWs. Insurance rates, parts and maintenance cost will only go up. And, as people already suggested, there's a variety of really good cars priced between a beater and M340: Miata, Mazda 3, Integra, BRZ.
If you want to get behind the wheel of M3 (as well as M2 and M4), sign up for
M Track Days. If I'm not mistaken, the closest to you would be Road America on May 9-12. It's not cheap, but it's a great way to experience M cars on a track without a headache of actually owning and maintaining one.