If you decide to go with a used bike, you are partly at the mercy of the marketplace and will have to buy what you find.
There are plenty of bike styles that are capable of a 2x10 mile commute. Look for:
- non suspension design
- tyre clearance for medium width rubber (28-32mm)
- threaded eyelets for rear luggage rack and fenders.
- gearing suitable for your speed, terrain, load. Race gearing may be too high.
- The correct size and fit for you
- Not worn out. Expect to spend some on tyres, cables, transmission, brakes.
Good quality tyres are essential on a commuter, they are the main cause of being late for work.
Consider a non-suspension hybrid, touring bike, some more practical styles of road bike.
Cyclo-cross bikes probably wont have made it to the used market yet, esp the really nice disc-brake ones.