Both, ME1 and ME2, can be done under 40 hours and you still have few days before ME3 is released. Or you can download save editors and create new saves.
If you decide to go with a fresh new char in ME3 (without any save editors or ME1/ME2 saves import) I suggest you look up the "default" choices your character made in ME1/ME2 (things like, have you saved the Council, is Ashley or Kaidan alive, etc.)
Here you can find all default:
http://masseffect.wikia.com/wiki/Save_File_Transfer
The best thing you can do (and also the rest of you) is to play ME1 and ME2 again. You will refresh what exactly happened and you can also include reading comics, which add some info about characters and plot between/behind the games.
You can do it in this order:
Play: Mass Effect 1
Read: Mass Effect: Redemption (prequel to ME2)
Read: Mass Effect: Incursion (prequel to ME2)
Play: Mass Effect 2
Read: Mass Effect: Inquisition
Play: Mass Effect 3
There are few more comics that you can go through if you find the previous ones interesting.
Mass Effect: Evolution (if you want to know more about Illusive Man)
Mass Effect: Conviction (sets after dlc Arrival)
Mass Effect: Invasion (sets after ME2, story about Aria vs Cerberus)
You will know more about characters, universe, background story, etc. and comics won't take too long to read, it is only a few pages.
*I didn't include books since they are much more time consuming and ME3 is here in no time.
** If you only want to play a different class in ME3, I believe there will be an option, just like with importing saves from ME1 to ME2, allowing you to change the class.