First of all, decide what type of vehicle will suit your needs. Are you looking for a traditional car in the form of a hatchback, saloon or estate - or a 'trendy' SUV type. SUVs make little sense for most as they don't drive as well and cost more to buy, run and repair - they simply aren't necessary. But obviously people still buy them. The one caveat would be something like a Skoda Yeti as mentioned above. They are pretty compact and very versatile with plenty of space inside.
The reliability ratings that have been posted above don't really mean anything in terms of buying a used car. They are using data from the manufacturer warranty which will be irrelevant and claims put to Warranty Wise which often won't cover things that are known to go wrong. Also, say for example an engine is burning oil or the gearbox is not quite what it should, it wouldn't qualify for a proper fix through a warranty claim, but those issues could see a car having to be scrapped in the not so distant future. The best way to gauge which vehicles are reliable is look at brands with longstanding reputations and research which are the best buys within those specific brands.
With regards to brands, Toyota and Honda have long been known to make the most reliable cars in the world. That's their petrol cars, they are of course Japanese and there are are hardly any diesels in Japan. So they've both basically perfected the petrol engine in terms of reliability going back a long way. Other brands to look out for are Volvo and Skoda/VW. Would avoid petrol cars with the latter. VW group put all their research into diesel over a decade ago and their petrol engines tend to have small engines and rely on a turbo. Their diesels are good but nearly all diesels across the industry post 2008 can have DPF issues amongst other things which can result in hefty repair bills. If going diesel, make sure you're not just doing constant short journeys, it can cause problems.
Some vehicles to look at would be:
Toyota Auris/Verso/Avensis (petrol)
Prius (hybrid)
Honda Civic/Accord/CRV (petrol)
Skoda Yeti/Octavia/Superb (2.0 diesel)
Volvo S60/V60/V70/S80 (2.0 petrol and diesel) but do research on engines.
From the above, Toyota will be the most reliable closely followed by Honda which will handle a bit better. Volvo will be the safest and Skoda will be the best for space and a good all rounder.
Another brand to look at could be Mazda (petrol). French and Italian cars are generally problematic as they age, they just aren't built that well. Nissan are generally much less reliable than Toyota and Honda.