Noise can be from the heat shield if it sounds loud, but there can be vibrations coming from the dash as this can the problem with this model. If you can still hear it when you turn your stereo it is probably the heat shield.
For the noise at the back get your rear arm bushes checked. This will usually clear the problem.
I had a curious leak coming through my head gasket and I thought it had gone. It turned out to be a leak in the inlet manifold.
Don't listen to folk slagging them off. They are people who thrash them and don't look after them! Keep it serviced and regularly check your oil and water levels. Always get unidetifiable problems delt with professionally (ideally Lookers Rover-I find they give the best service!) Problems can sometimes be caused by more than one fault. I took my car in for a clutch and a water leak. I found that the clutch was contaminated by the leak that I had in the inlet manifold and a bearing in the gear box. Since the work the car works like brand new.
My car makes a noise at 3000rpm near the alternator/exhaust manifold, but I just ignore it, Rover said nothing about it and they checked it thoroughly!
A Rover family, well I work for Honda so no problems with faults on my wifes 216. Yes, remove the heat shields from the cat.
Check the trailing arm bushes, they go soft and break up. Check the rear caliper slides.
Otherwise a little belter of a car. (Mine is a 214!!!)
All a lot better and cheaper to run than my previous Volvos and Legends!
I Bought a 94 Rover 214 SLi today as a cheap runabout. Full history, average miles, GSi Trim level. One of the posters is quite right, If you look after them, they can and will last a heck of a long time. I have bought many cheap runabouts over the past few years, and I can honestly say that the car I bought today is the sweetest of them all. One thing though, as with many pre 96 Rovers, watch out for the electric Windows, they have a tendency to come off the runners, and also I was advised to have the Head Gasket renewed, but I have a service report showing this being done last year. But overall, the 200 and 400 series is a comfortable drive, and I look foreword to looking after my 214 for the foreseeable future.