Mileage - try to buy something that's under 50,000 miles. I'm guessing you're going to be looking into the plastic econobox market. There's quite a few low mileage (suprisingly low mileage for the year - 20,000 or so) plastic econoboxes around.
You also need to consider how the car has been used. Don't necessarily be put off by a 3 year old car that's done 70,000 miles (Example: My dad has a 70,000 mile 2007 Saab, and it's absolutely mint condition). Usually the case with cars like this is that they're medium to large saloons that have been up and down the motorway all day long. These can be in better condition than your average 40,000 mile car, because there's not the constant wear and tear of climbing in an out of the car, they haven't been scratched and dented in car parks, and they haven't been driven around town, never getting up to temperature.
Likewise, if a car's done 30,000 miles and it's an absolute dog, don't immediately think it's been clocked. The likelihood is that it's been used by a messy family with some toddlers, who only do short journeys and haven't cleaned their car since they bought it new. The ultimate sign of genuine high mileage is the super shiny steering wheel. Although first check that this isn't silicone spray, which some imbeciles just spray all over the interior, thus making everything greasy and shiny.
The bottom line is, when you come to sell your car, it will be much easier if it is lower mileage.
Number of owners - You don't want a car with 5 owners in the log book. End of. Be careful of the wording of adverts - 2 previous owners isn't 2 owners from new, it's 2 owners + the current one, and then you will be the 4th owner
Main agent dealers - For the love of god do not buy from one of these unless they're offering you some super awesome warranty plan for free. Main agents typically charge several thousand more than smaller traders and private sellers. This rarely equates to a better car or a better level of customer service. They can only charge more because they have the brand name behind them, and people trust them more than other dealers. Even if another dealer may be just as friendly, just as helpful and just as trustworthy.
Scratches - All used cars are going to have scratches and minor marks on them. If you look round a used car as if it's a new one (like many of my dad's customers do), you're going to be dissapointed. And you're also an idiot.
Dogs and Smokers - Unless you are a smoker yourself, don't buy a car that's obviously been used by a smoker. The telltale signs are a strange mortuary-esque smell which is a mixture of cans and cans and cans of air freshener and cigarette smoke. It is near impossible to get the smoke smell out of a car, except by airing it out FOREVER
You also don't really want a car that shows signs of dogs being shoved in the back of it on a regular basis. There is of course the smell of dogs (not quite as bad to remove as cigarette smoke smell), and the scratched windows. If the dogs have scratched some of the heated rear window element off, that's quite annoying.
Service History - You want to make sure that it's been regularly serviced. Don't be put off if it doesn't have the main agent stamps in it. All that tells you is that the previous owner didn't want to spend hundreds and hundreds of pounds on what is a simple job that any garage (or more like anybody) could do. Full manufacturer service history is more important on newer and more expensive cars, but I'm guessing that's not your sort of car/price range?
I suppose i'm looking at this solely from the point of view of having to sell it after a few years of ownership. If you plan to chuck it in the bin after using it, you can ignore full main agent service history (although you still want a car thats been well looked after), and you can ignore the number of owners.