You'll be lucky to get a Type-R with 65-85k on the clock for £4500 unless you're prepared to buy a Cat C, which I would definitely not advise unless you know exactly what happened to it. Maybe one with 100k miles is more optimistic (which in many cases is as bad as a Cat C looks-wise). I started out with a budget of 5k not long ago, but I got so sick of looking at so many wrecks in the end I just bought an absolute beauty final edition for 8k. It's really not worth spending 4.5k on a car that's on it's last legs, if you can, try spending a bit more on a beauty that'll last you longer and is therefore cheaper in the long-run.
Advice when buying - ALWAYS have it HPIed - of all cars Type Rs are the most important to have HPIed as I find they are more likely to have dodgy history than any other car, especially for that money. Also - if it looks nice on the inside/outside, be wary as garages are notorious for changing the gearknob/seats etc to make it look nice when the inside it actually falling to pieces. And garages do not know how the car has been treated previously, no matter how much they claim to. One man at a garage gave me an obvious load of bullshit about the type R just being "hard on the steering to improve the handling" when I know for a fact it was pulling to the side. Out of interest - that car was selling for 13k at the garage, when I bought the EXACT same in better condition privately for 8k. Lesson learned - buy privately.
Also, if you are looking at a lower budget, I would advise buying a silver Type R as they are cheaper than all the other colours. (I think it is the only type of car I have seen colour make THAT much of a difference and I'm talking anywhere between £250-£1000), though the garages don't seem to recognise this, autotrader prices sure do.
Also, with type Rs, and in particular a low budget, do be prepared for some damage. Be wary of NHB owners who haven't cleaned their car. A clean NHB shows off anyyy problems/scrapes/touch-ups very nicely.
One last piece of advice - it's good to meet the person you're buying off to see what kind of a character they are - are they likely to have mistreated it? why are they selling it? do they obviously care for the car? A high owner-turnover = bad news. It's much better to buy a type R from someone who has had it a long time. If you are buying it off someone who is selling it after owning it for 2 months, alarm bells should be ringing and there could be a problem with it.
One last point, sorry to break it to you, but I think with that budget a face-lift model is out of the question unless you are prepared to wait a loooooong time.
Hope this helps, and I apologise in advance for the lack of technical terminology. If I have got anything wrong I also apologise.
Sarah