New car, some problems

[Mad Cow]

I just bought a '97 328i with 227k km's but it has a few problems. First and foremost is that the engine vibrates like hell between 1k and 1.5k rpm in neutral or with the clutch in. It still vibrates in gear but it's not as bad. Apart from the vibration it seems to run fine, it has plenty of power and isn't misfiring or anything. Could it be a horribly worn motor mount?

Another problem is that the shifter vibrates when it's pushed all the way to the right and it feels sloppy going into 5th gear. I'm thinking shifter bushings, but I don't have much knowledge of longitudinal engine shifter setups, so which bushings should I be looking at replacing? Will buying a short shifter (which is my first planned mod) give me the bushings I need?