Sounds like you’ve got some mess on your hands. One step at a time:
Get your hands on a good pressure washer, if possible. After pressure washing, allow to dry.
Still got sticky crap on the floor? Get some adhesive remover, like Jasco Adhesive Remover - it’s available in many places, including the big box stores, or they should have something similar. Follow the directions, but if I’m remembering correctly, you let it set and then scrape away at it with a putty-type knife or something similar. With a little luck, the pressure washing should have made this easier so it doesn’t seem like such a huge, daunting task.
Still greasy crap left over, even though the adhesive is gone? Use a concrete cleaner, like Seal Krete OSR.
Etch it with something like Seal Krete Clean N Etch - avoid the muriatic acid at all costs. Unless you are a professional or are hiring a professional for it, just stay away from that stuff. It’s acid. Seriously nasty stuff. The Clean N Etch will give your concrete a profile and prep it for staining.
Hopefully the floor is looking less skanky at this point. From here, you should be able to get any manner of concrete stain. Obviously, the line I’m familiar with is the Seal Krete, but there are plenty of others. The Seal Krete has the bonus of having a water-base, semi-transparent stain, but you may not want to see the old concrete. There are pros and cons to the stain you choose, be it oil base or water base. Oil bases tend to be slippery when wet, and may need a gritty additive (Tred Tek or Clear Grip or along those lines), and water base, while they have lower sheens, may not have as much durability over time (Cabot and Sunproof (PPG) both have a nice latex solid colour stain, usually used for decks, but you can use it inside). These are, of course, simply the products I am familiar with, do some research and see what’s available to you.
It is a bit of work, but you can make it happen. Good luck!
An expensive option: talk to a contractor who does industrial coatings and have the thing bead-blasted and use Mega Seal (PPG) on top of it, holy cow, that stuff looks awesome. I know, I know, probably a little over the top for your project, but boy, does it ever look sweet.