I'm not in an EMS or SAR position but I have looked at them as civilian work a bit.
First suggestion I'd make is to go Military since that is the most sought after experience for SAR and Med at the moment and there is no monetary cost to you (does cost liberty and might cost your life, but that's aviation in the civil world too!).
Otherwise, I went the FAA route at HAI (as it was called then) and found the JAA conversion to be straightforward if lengthy (and expensive for the JAA IR conversion). Personally I enjoyed the process since living for a couple of years in the US suited me (in fact if I could go back I would!). It may not suit everyone though...
Note that I didn't do the JAA/FAA route in the US - I just did the FAA and converted it when I got back. As a result I got more hours since I was able to get the FAA stuff done quicker and start working on the time left on my Visa (about 12 months as opposed to 6 months or less if you do the JAA course). The downside was about 8 months back in the UK converting while not being able to work.
As has been stated - don't expect to save much money overall but I found I ended up with more hours for that money (having gained experience in the US) and therefore closer to employable than spending the same money and time the UK.
Good luck anyway!
BG.