I just completed my first Mass Effect playthrough and while I won't be doing this immediately, I will most likely go back at some point and play through one or two more times. A few questions for those who are hopefully more knowledgeable than me. 
 
Can I start an entirely new character and have the ability to import either or both into ME2? I played a male Shepard and would like to play a female one (really didn't care for the male voice actor), but I don't really have a good sense for how the import works. If I start completely new character will I be able to later do a New Game + at all with my old character?

They are different saves, every shepard that completes mass effect 1 can be imported into mass effect 2.