Rich,
Being more in the Black Country to be honest I haven't visited and explored the actual city of Birmingham much, but I am about 20 minutes outside it. So, I am not sure what areas you are looking at but from what I have seen from when I looked into living in Birmingham and commuting, it can be a bit pricey. I was looking at furnished flats because I didn't want to bother with furniture, at least for the first few months. Most of the furnished flats I saw online were 500-1000GBP. This was in the process of looking with a potential roommate so I was looking at 2 bedrooms and her taste was a bit fancier than mine. I will disclose that my flat is just over 400GBP a month, furnished. It is a size that could work for a couple, but I think much more happily inhabited by a single girl as myself. I think you can definitely find a nice place in a nice area in Birminginham for the prices you are looking at but I would look into the area. It is very clear once you arrive how the prices coordinate with how nice the area is supposed to be...Of course, I think this can be open to opinion as well... I will try to ask a work friend that lives near Birmingham City Centre to hear her thoughts. I have found more luck with asking around to locals once I got here than anything else. And, I don't want to give you any loaded advice as I am not extremely familiar with specific areas in Birmingham. If there are community papers once you arrive surrounding where you will be at school those seem to be the best (in my area) for finding what's on in terms of lettings.
The biggest thing I learned in moving here and finding a place is you can't do much until you are actually here. You'll get much better response from Estate agents and a better idea of what you're looking at when you get here. If you can, I would reccomend setting up temporary accomidation to give yourself sometime to find the right place. I arrived 12th of Jan and was in my flat by 19th of Jan so it doesn't take long!
Good luck! What are you studying, just curious? If you and your fiance arrive this summer, hopefully I will be more familiar and help out if you have more questions!
lisa