Change oil every 10 000km. Consider using Liqui Moly 10w60, many M3 users have moved over to this oil, including myself and are very happy.
Do not rape the car right from cold start. Warm the oil up before any revving past 4000rpm.
Check with BMW that the car has indeed done bearing recall if it is 03 model or older.
Also, depending on the age of the engine, consider doing Vac coated bearings and uprated oil pump for peace of mind.
Listen for a ticking noise on the engine. If the sound is present, the engine will require valve clearances to be done. This happens to ALL e46 M3's. I also suggest getting a guarantee on the work being done, as my car went to Savspeed for valve clearances and they botched the job. Valve clearances or valve shimming, is very straight forward, but can result in massive failure if the incorrect sized shims are placed into the engine. This is what happened to my car and this resulted in my car dropping an exhaust valve in cylinder 6 two days later. Savspeed refused to compensate me for the damages. I had replace one cylinder, one piston and a new cylinder Head. This job was also botched and required me to eventually seek out a full engine rebuild by a member on this forum. Thankfully, the car is running now and back where she belongs. So make sure you get a guarantee on the work being done.
Check rear subframe for cracks. Go to
http://www.redish-motorsport.com/ and watch their videos on how to check for cracks.
The convertible was considered to be less prone to these subframe cracks, but it can still be possible.
When test driving the car, place it into 6th gear going up a gentle hill and accelerate. If the car does slowly increase speed, she is healthy. If not, you may want to look at Vanos seals etc. Speak to A1exander on the forum about this test.
Tyres for these cars are not cheap if you want to keep the car at peak performance.
I can speak from experience in regards to all the above steps. Good luck. The e46 M3 really is an amazing car, and as much as all the above sounds daunting and scary, you need only be wary of what
may happen. Abusing the car and not respecting the fact that it requires a warmed up engine before fast driving and that the rear subframe be looked after, will result in these problems appearing.