There are cheap solutions but its worth while doing properly (isnt everything?)
You need a bullet cam - they are all different qualities but look for a good "TVL" number (a bit like resolution is for a digicam) 480 TVL upwards is good. 520 TVL is near DVD quality and so on.
End pic quality will also depend on how you actually record the image however (no point having the worlds best bullet cam if its then recorded on to an EtchaScetch).
There are a few ways of capturing your image.
DVR (digital video recorder) with hard drive (prone to jumping if bumpy)
DVR with flash storage
Camcorder with AV in (MiniDV seems to give best results)
MAKE SURE YOU HAVE "AV in"
How much you pay is a tricky one. You can pick up a good 2nd hand MiniDV camcorder on fleabay very reasonably. There are also some camcorders that record to flash (Vivitar I think). The sky is the limit tho. Ive seen some systems that cost 1000 pounds!
Some other options are power packs, remote control (LANC or wireless), Mounts.
My advice is to do LOTS of research before you spend. I was on Google and talking to M8s for about 3 or 4 weeks before I took the plunge.
In the end I got a bulletcam from DOGCAMSPORTS and a Sony DCR-HC42E camcorder from ebay.
Here are a couple of links to get you started:
http://www.dogcamsport.co.uk/http://www.4kam.com/http://www.rfconcepts.co.uk/(all good sources of info even if you dont buy there)
Im by no means an expert, and I still take all the advice I can get when it comes to this subject, but I hope the above is useful to you.