Not the transmission, it's the center support bearing most likely - and possibly the flex disc.
It's the part in the middle of the driveshaft (center bearing) which is about $50, and the part on the left side (flex disc aka guibo, about $45.)
Repairs aren't hard unless your exhaust was 'welded' together thanks to rust. Took me 3 days to cut the rusted down pipe bolts off of my exhaust. I am 99% positive it isn't the tranny, I don't hear about E30 tranny's failing or having problems with vibration.
I also bet the noise is worse when you make a turn. What happens is that center bearing, which the bearing holds the front driveshaft half over the splines (you WILL need a large gear puller, $15 at an auto parts store), and then that bearing is held in the Center bearing housing via semi-hard rubber. I'm sure yours looks like what mine looked like - the rubber was gone and the driveshaft could be moved up and down a few inches.
Here's a pic of it on my car AFTER being replaced.
Flex disc attached to tranny (HOLY gear selector seal leak, batman!)
http://www.bmwchannel.com/eric/clutch/100_5805.jpg
and then center bearing
http://www.bmwchannel.com/eric/clutch/100_5806.jpg
front half removed with CSB and flex disc
http://www.bmwchannel.com/eric/clutch/100_5809.jpg
If you don't have one, buy a bently manual $35 from
www.bavauto.com - which I reccomend for parts. EXTREMELY fast shipping to me in lancaster, PA, so you're not too far away from me. I'd typically get my stuff the 2nd business day after I order. If you EVER need help, especially with drivetrain repairs, shoot me an email or IM me on my aim SN (it should be in my profile by clicking on my username).
It's a shame that after all the knowledge I've gained on E30's - my car is now wrecked. There's no "smiley" appropriate for that