Can I get to level 60 in the first playthrough of Mass Effect?
Solution 1:
No, you cannot. You are limited to a level of 50 in the first playthrough. The level cap will be raised to 60 subsequent playthroughs. Reaching level 60 will require more than one playthrough regardless since there is not enough experience to go from level 1 to 60 in 1 playthrough.
If you do not mind loading in someone else's save files, there is a nice site that allows you to choose the storyline options and completion % for ME2 import.
You will be able to change the look and class of your imported character in ME2.