Hiya
I'd suggest you nip into WHSmiths and pickup a copy of What Car magazine. They have allsorts of guides, info, tips into buying a used car both from a dealer and/or privately. Soak up as much info as you can and then venture out to view and hopefully a little while later buy.
There are new schemes for 'pay as you go' insurance but as yet I think they're only in the experimental stage, I haven't looked into this myself as yet because it's not mainstream enough, plus I know I need the car often everyday. Unless there's some good bonus I'm going to wait till it's more widespread. I'm sure that even if you can get a policy for pay as you go now, there'd have to be some minimal cover for when the car is parked up - I doubt it'll only cover you when you're actually driving only, as when parked what if it got stolen?!
I'm pretty sure that once you get your UK license, any speeding tickets in the US won't be applicable here, if you drive on your US licence for a while here, am I right in saying the details of the ticket dont show on your actual license? and the only way to find out it call/contact the driver licensing people there?
Buying privatley can save you quite a bundle, but you need to know what you're looking for and the golden rule is to use your mind over your heart when buying - it's so easy to have a 1st choice car you really like and when viewing one get your judgement clouded! - there's more risk in terms of comeback when buying privatley, but the trade off is you paying much less than a dealer's forecourt price. Buying from a reputable dealer is the safest, and of course most expensive. read up on the magazine tips and guides to get more info - you'll feel better and more confident!
www.autotrader.co.uk is a very good site indeed and all the info you could want to know about buying a motor is on there too, plus you can search out car's for sale and work out budgeting etc as well.
As others have pointed out, alternatives could be just hiring a car when you need it, it's relatively simple and quick to do, I'm going to look into Kristi's suggestion of 'city car club' ( I think that where you jump into a little city car, drive it to wherever and leave it when you've reached yer destination ready for the next bod to drive it - but I could be wrong!)
Cargiant I've been to a few times, great selection to view, sit in and get a feel for, test drives of course as well, and all the finance stuff, their cars usually are direct from the Auction houses or ex lease etc, can be hard to find a low miler but they are around!
another cheap place is 2 miles from my house, called 'Trade Sales'
http://www.trade-sales.co.uk/my business partner only yesterday bought a 8 month old VW Polo for his other half from there - one of the biggest and cheapest places to buy a car from in the UK!
Hope this helps!
DtM! West London & Slough UK!