I highly recommend the Toyota Corolla. It is the most common car in the world. (Some 40 million Corollas have been produced worldwide)
I have a 1997 Corolla with 1.6L 3 spd auto, with 196,000 miles on it. I see so many of these cars still on the road. I purchased it with 134,000 miles about 5 years ago from a dealer for $4000 including Tax/Title/License. In this time my car has only not started once (loose battery cable).
1996 and 1997 models have OBD-II connectors. I am not sure about anything earlier. This is important if you want to connect a ScanGuage II or to get Check Engine codes.
What I like about it:
Toyota Quality - I work on the car myself. Everything is so easy to work on. It does not require a large tool set. It is not especially rugged or flimsy. Everything on the car was designed for economy, which is great for EcoModders. Classic Toyotas are known for longetivity. 200,000-300,000 miles on the original engine is not uncommon. Classic Toyotas are very reliable and are not subject to the current Toyota recalls.
Size - Compact - Great for fuel economy, but still much roomier than ultra-compacts like the Geo-Metro. Curb weight for a 1997 Corolla is around 2300 pounds (light enough for good mpg, heavy enough to have a good feel while driving). Later models are considerably heavier.
Engines - Available in 1.6 or 1.8 L for that year. MPFI, 16V DOHC
Transmissions - 3 speed (I don't recommend it, although I can still get great gas mileage), 4 speed auto, 5 speed manual
Tires - 185/65R14 or 175/65R14 stock. I run the 185s in a Pirelli P5 with 85,000 mile warranty. They cost $74 each for the tires. My ride is so smooth and I have nothing to worry about for a long time. I live in Texas. We have about the worst roads in the world. I understand the advantages to running an ultra-small wheel, but I think for safety it is better to run a normal size tire where I live.
Upgrades - There are actually a ton of aftermarket parts for Corollas. Parts for Corollas are usually pretty cheap because of how many of these cars that were produced. Most parts can be replaced by just removing a few bolts. (Like the suspension upgrade I just did. 6 bolts per strut, too easy)
Here is a Corolla with way too many upgrades:
http://www.cardomain.com/ride/653609/9
Safety - Driver and Passenger air bags are available. Everyone in Texas has a giant truck. The corolla is the smallest car that I feel somewhat safe driving on freeways here.