It's already been partly painted over the years... So just looking to make it one color.
You're basically hooped with it having been painted before. Anything you put over top is going to rely on the layer below for adhesion to the concrete. So, unless you grind down to the bare concrete, don't expect anything to last long term.
For the archives, on a bare (new) concrete floor: I moved into a new house six years ago with a massive garage. Our townhouse is built on a floodplain, so legally they can't put living space on the ground floor, instead you get massive garage! (perfect for those of us who are car crazy.)
Our garage had been driven on by many a realtor, but it had not been dripped on as far as I remember. We followed the proper steps for application:
1) Wash floor with soapy degreaser product.
2) Wash & scrub floor with muriatic acid.
3) Apply paint with roller.
We were on a bit of a time crunch, and moved into the garage after just a 24 drying period. And when I say we moved in...we MOVED in. Two rally cars, 8 mountain bikes, an entire shop worth of tools, 3 tool chests, sandblaster, one whole wall worth of shelving and bins, engine hoist, engine stand, two work benches, tires, air compressor, spare engines (x2)...the list goes on.
I have rebuilt two rally cars in the garage, swapped out too many engines to count. Built and painted the white bug, more engines, then built the Salzburg bug in this garage. I've dropped engine blocks on it, welded enough to use two large spools of wire, spilled every type of automotive fluid on it you can imagine and yet the floor has held up 100%.
Brake fluid, we discovered, will soften the floor paint significantly. If you clean up the fluid, and leave the floor to dry...it will REHARDEN. You can't tell we spilled brake fluid on spot number one. Spot number two, however, where we didn't know for a day or two, there is a dark spot due to dirt getting mixed into the soft paint.
Other then that, the only other stain is from four years ago when I drove the rally car over a sharpie marker and didn't notice. I've got a blue stain on the floor which I've pulled half up using rubbing alcohol. Geoff will attest to the fact that the grey can look dirty with a lot of use, but a good scrubbing and it comes up looking fantastic.
HIGHLY recommend this product.
Pratt and Lambert PalGuard 2-part epoxy paint.

Some shots:
Laying the Paint (Base 1 - S3401, Gloss Activator S3498)

Initial Move In

Rebuild #1 - Finishing up near ice-racing season, so the garage is a little messy


Rally Build #2

Griding and welding...

Lots of 6-years later, haven't washed it in a year, shots in my Salzburg build thread.
-Dave