If you are a family of three then you won't necessarily need a large car, so we would consider looking at cars such as the Toyota Yaris and Honda Jazz. The second and third generation Yaris used a torque converter automatic and is generally considered to be a very reliable car, and while the Jazz uses a CVT (excluding 2009-2011 cars) it also has an excellent reliability reputation.

For non-Japanese options, we would suggest looking at the Hyundai i10/i20 and Kia Picanto, mechanically similar cars which also used a torque converter automatic and are cheap to run as well as reliable. All of these options were popular so you should easily be able to find several examples within your budget.