3 miles is towards the shorter end of a worthwhile bike commute but its still more fun than walking.
You dont need anything special but it should be cheap, practical, low thief appeal, reliable.
A standard hybrid style bike is fine. You wont get there any quicker on other types of bike.
You dont need front suspension but its hard to find a hybrid with a fixed fork these days.
Make sure you have threaded eyelets for luggage rack and fenders. For 3 miles I would use a backpack BUT with a luggage rack you can do heavier shopping trips.
Upgrade the tyres to the most puncture resistant you can find, such as Schwalbe Marathon Plus. I wouldnt bother with a repair kit for 3 miles, you can walk your bike to work quicker than change a Marathon Plus tyre.
I like a grab and go city bike with all the accessories secured to the bike so I dont have to strip it down at every stop. Some people remove their wheels, seatposts, lights etc at every lockup.