You are referring to he invariant mass, m0
, which you are correct, doesn't change in different speeds. Rather, it is inertial mass(or relativistic mass), the object's resistance to acceleration that increases with acceleration, so that:
ER = γmc2
is the relativistic energy.
So the same conclusion still holds: as you approach c, you require an infinite amount of energy to reach c itself.
I tried to simplify it for the person asking the question by just using the term "mass", mistake on my part.
EDIT: Oh, I forgot to say: You're right about time dilation preventing you from going faster than c, there are several other factors. Obviously, the Universe is pretty strict on maintaining it's speed limit.