Ive been meaning to reply to this thread for a couple of days now, but haven't got round to it so here i am.
As Grim said, yeah i used to have a Clio, it was one with one of the bigger engines in the 1.8, was a fast little nice car in general, however due to the age of the car (was on a J plate) there was problem after problem, personally i don't think Renault helped with their wiring loom in the car in general, it looked like an 8 year old made it at home and bodged it in, not that it had ever been messed with either they are all the same. The car cost a small fortune to keep right and on the road, and everything it needed was always done correctly.
My personal advice would be to be spending at least a minimum of £1000, if you can afford £1500 then do it, the more you can spend on a car in the first place the better for you. You'll soon get the benefit of having a nicer, newer car without having to spend a small fortune on replacement parts all the time.
The owners of alot of older cars usually say thousands spent in the last couple of years keeping it right, in my opinion it says the car has been looked after, but if they have been spending so much on it, it basically tells me its been looked after to an extent, but the owner(s) are obviously fed up of spending on it all the time and want something newer and more reliable.
You can get horrible problems with second hand cars in general, new and old, but the odds of getting a car with alot of problems would deffinatly be an old car.
Grim and TS have given you some good advice, i'd consider everyones opinions very carefully aswell.
Oh and i appreciate why your considering a 1.0 engine, but seriously i think after a few months you'd be really fed up with it, in a small car i'd want a deffinatly minimum of a 1.2 16v if possible i'd always go for a 16v engine over an 8v (engines size for size tend to be more powerfull when using 16 valves)
Also even if you spend up to £1500 on a car, third party insurance will be your best option, probably better if you can cover yourself against fire and theft due to the facts older cars tend to get stollen often as their security on alot of them is almost next to none.
Although this isn't directly related to buying a car, i'd also recommend you buy a good steering lock. I'd never leave my car without the steering lock in place, it will really help when it comes down to car theft.
Oh and as for car recommendations, the fiesta MK5 is a nice little car, you should be able to pick up a reasonable example for not too much cash. I'd recommend you look at the 1.25 zetec model
but of course there are a few different models to choose from.
I know Grim in particular isn't too keen on these, but the Vauxhall Corsa B is a cracking little car, the 1.2 SXI is a great little run about, though the SXI badge does tend to affect the insurance a little. Still, its a great car and has a few nice features. The Corsa C i personally don't think looks as nice, but isn't a bad car none the less. I can vouche 100% for Vauxhall, they are a great company and make great cars, currently me, my brother and my dad all have Vauxhall cars, my brother and my dad have had Vauxhalls for years now and they are without doubt (within reason obviously) some of the most reliable cars ive ever seeen.
VW isn't such a bad company either, they have a nice few small cars, the polo has been one some young drivers seem to go for, so might be worth looking into, though i can't comment too much on them as ive never owned one, though ive dealt with them before.
Just to also note, as Grim mentioned, pistonheads is a great website, deffinatly worth your while doing alot of research on it so you have a rough idea of what your getting for your money. Also deffinatly remember, virtually every car thats for sale if you ask people about them they all reckon they are in great condition in and out, however usually i find it very dissapointing when i arrive to view the car.
Remember well what TS also advised you on, remove the oil filler cap and have a look in there, if there is any sort of gunk and its not nice and clean stay well clear. I'd also check the dip stick and see if the sump is full of oil, if its looking low i'd want to know where its gone.
If you do a test drive, i'd like to rev it well out while on the move in 1st and quickly shift into second and put my foot straight back down, at this point look in the rear view mirror for a swirl of blue smoke or smillar, this will give a good idea as to wether or not its burning much oil.
If the car has ABS, be sure to check the brakes and make sure that is all working correctly.
In the event the car has air-con check that and make sure it gets nice and cold, as on older cars they tend to need a re-gas on an older car i wouldn't expect it to work properly unless its had a service and most of them don't. This can of course be a good haggling point if the air-con doesn't work.
Be sure to check in the boot, lift the boot carpet and make sure there are no creases or odd looking repairs in there. If the boot floor is creased i'd walk away at that point.
I know there are alot of older cars that have had minor accidents, or have been wrote off then repaired, i'd try and keep clear of any repaired write offs alot of them can be dangerous, or possibly full of problems. Always try and check the history of the car before buying, there are services online where you can pay, enter a reg number and it'll tell you the history of the car. On this note also watch out for cars that could possibly still be on finance, you don't want to buy a car someone is still paying for, if they stop paying for it the company will come and collect the car from you and you'll have lost your money.
I think these points and the ones others have mentioned should get you well on your way, TS put some good check points out aswell about un-even tyre wear etc, if the tracking is out i'd like to know why as its probably suffered a good shock or wear.
Sorry for the slightly long post, i'm sure there is more i could add, but for now i'll leave it at that