Question

what gives light its speed

Answer 1

When photons collide or reflect they are actually in a sense being absorbed (annihilated) and a new photon is emitted (created). In this case the first photon provides the energy to create the second one. Your first sentence is correct. You said acceleration to light speed takes infinite energy - yes its true.

Answer 2

Light is actually the movement of special particles known as photons.
These photons have high amount of energy and momentum.
So due to the special theory of relativity.
Light gets it's high and incredible speed.