Might also be worth looking a touch above your price bracket as the advertised price is very seldom (if ever!) the real bottom line. A lot of cars advertised for €3k may be sold for a €2500 cash deal (if you keep an eye on the adverts [on websites, magazines etc.] a car which is there a few weeks has a good chance of going well under the asking).
If you have friends or family good with cars make sure they do a good inspection. If not, might be worth spending the couple of hundred euro on a mechanic to go over the car for you and save you spending the €2500 on a "lemon" (as it's known).
The best thing to do is use the car websites to begin, you can filter the cars to the price you want and throw in any other options (e.g. oldest car 95 etc.). This will show you what cars are in your range and then you can start to pick out the ones which you prefer from there.
The older you go the larger/more prestige/etc. the car you can get, but reliability (and future costs) tend to go up with age. The suggestion of a nice second hand japanese motor would be a good start (Nissan, Honda, Toyota etc.) but don't limit yourself too much until you get an idea of what you like/want.