You are technically travelling at 99.99999% of the speed of light right now, relative to something.

You are actually traveling faster than the speed of light relative to some distant galaxies. The "speed limit" in special relativity refers to an inertial reference frame (in general relativity, this would be a reference frame with no/negligible spacetime curvature). As soon as you have significant gravity/acceleration relative to things with mass, the answer becomes much more complicated (and not fixed).

What determines my speed limit? Is it set at 0 here on earth? What if I travel to another galaxy, this one was going at .5c relative to me when I was on earth. Then after trillions of years, inflation causes all of the galaxies to separate beyond sight from me in this new galaxy. Now, the centre of this galaxy appears at rest. Does my velocity get "reset?"

Special relativity says that no matter what your velocity is relative to Earth you can proclaim that you're actually at rest and it's the other guy that's moving. So your velocity is always continuously being "reset". And in each of the frames of reference of everything in existence nothing else is traveling faster than the speed of light.

The 1905 Special Relativity Theory (1905 SRT) version of reciprocity implies that the other guy in a different inertial frame than your own will be the one that is moving. The consequence of this implication is the "Twin Paradox" (i.e. both twins in different inertial frames have been accelerated and are both aging slower than the other twin). A different version of reciprocity that implies that the accelerated twin is moving and the apparent movement of the twin that has remained stationary is only an aberration (or mirage) is axiomatic because movement first requires acceleration.

Assuming spacetime is not expanding, let's say 1 galaxy is moving away from us at .9c. I leave our galaxy and catch it by travelling at .99c. Then a citizen of that galaxy, at rest, accelerates to .9c. So his velocity relative to earth is .89c? I think I need to go watch a youtube video on special relativity. Intertial reference frames are really weird.

inflation/expansion of space is not limited to the speed of light.

I know. That understanding is already illustrated in my question... I don't see what that has to do with answering it?

As far as we know, as long as you don't actually reach light speed (which is currently thought to be impossible anyway) you can pretty much get as close as you want and be fine.

Thanks. It's quite counter intuitive to think about. You'd be going along at 99.99999999999999999999999999999999% and then hit that last bit and poof now I'm photons.

Well, achieving that "last bit" takes an infinite amount of energy, so it's not surprising that that has some effect.

Yes, as long as you don't hit anything or care about the time dilation you will experience.