For 2 mile journeys, folders are OK, but get a decent one. Some of the cheapie models will get shaken to death.
An older "beater bike" works well. These can be picked up cheap, and if they were good when new, they should still ride well. Make sure you can fit a luggage rack and fenders. Singlespeeds are light, simple and reliable, hub gears (3, 5, or 7 speed) are clean and easy to use, MTB style deraileur gears (3x8 gears) are overkill for the city, but if they come with the bike, use them.
You can leave an armoured high security chain at each end of your commute, and carry a smaller shackle or cable lock for stopping off at the shops.