Unless your considering a basic and old Honda Civic the only car in that list that really wouldnt eat into house funds is the MX-5 imho. The s2000 is in a completley different league for insurance (for myself its an increase from £800 to over £2500) and you have to pay considerably more to get a good one than you would an MX-5.
I think you need to consider your priorities, you cant realistically save for a house and buy a 2010 Honda Civic with less than 5000 miles on it........... A quick look on Auto Trader suggests the bare minimum for that spec civic is £11000, for that money you could buy a Z4, S2000 AND an MX-5!
Why not step the budget right down to say £5-6000? If you have 12k sitting around to be able to afford something you could quite easily by yourself a fun or a practical car and still have a good 50-60% of your capital left for the house deposit.
A couple of fun examples;
http://www.autotrader.co.uk/classified/advert/201134411957420/
http://www.autotrader.co.uk/classified/advert/201145427203763/
Or something sensible;
http://www.autotrader.co.uk/classified/advert/201126395695742
http://www.autotrader.co.uk/classified/advert/201140419410387
In regards to living with a soft top day in day out, I've never found it an issue as of yet. Yes its a bit noiser and colder but the car more than makes up for it. In terms of security, are you going to worry about your windows all the time if you have a hatchback or hardtop? It's just as easy to smash glass as it is to slash a roof.