In general, $2,000 highly reliable cars don't exist because any highly reliable car is worth more. Buying from a dealer it's probably impossible to find such a car, since a dealer needs to earn at least $1k to keep the doors open.
For cars old enough to sell for $2,500, how it has been cared for will be extremely important. Look for a car that's not in much demand but for which the owner has a thorough maintenance history. And be sure to get it inspected by a good mechanic.