What you'd need can't be found at a tool rental place. It'd take a terrazzo grinder with a couple of different grits of polishing stones. Even if you COULD find one for rent, you really need to know what you're doing to run the machine. All it takes is a split second of inattention during a process that's extremely monotonous and you could ruin the floor.

There are many overlay systems that work well with patched concrete. Staining and Polishing can also be done if the patch was done well. The difference in the age of the patch and the old floor may be an issue for just polishing, which is why I mentioned the overlay possibility. A 'skimcoat' is often a latex product that will not polish well. In this scenario an epoxy finish or overlay would be a better approach in my opinion. Somewhere like floridaconcretepolishing.com may be able to guide you further. Here is a link that might be useful: florida terrazzo repair

It's probably best to find a dedicated decorative concrete contractor and rely on their advice. Just like with other contractors, check their work and get references. Because most concrete floors are commercial, you may need to reach into that world to find the right experienced professionals. Just as with builders and designers, you are more likely to get a better response if you offer to pay for their upfront time and it's usually a good investment. As I mentioned in Russ' recent concrete floor thread, it's tough to keep up with all the advances in this industry. There are many combinations of techniques and products. I think Jannicone, that you are after a less variegated and contrasting surface, so polished may be better for you. A light grind that doesn't penetrate past the paste layer will still give you some opportunity to add color with a stain or dye. Sounds like you may prefer no color or stain in which case I would consider including a decorative aggregate in the mix or seeded into it while finishing. The top coat, sealer or topical guard is a big decision and would rely on the decorative contractor and retailer selling the product. I do think a penetrating sealer sounds ok for your needs but fear you will still be told that it's never good to let spills sit for more than 30 minutes. An epoxy sealer could be the answer here and there are many products promoted to handle harsher chemicals. I would try to get the decorative concrete contractor on the same page as the finisher, often they serve the same roll. You could use an epoxy sealer without polishing, just don't let the finisher use a seal and cure product. Rely on water, burlap and plastic for a good cure instead.

It's true that in many jurisdictions, converting a garage to living space isn't permitted. However, if you live in a rural area or some place where it is legal, I have seen concrete floors that are stained and finished beautifully over large surface areas without any extraordinary slippage issues and fairly thin coating on top. You'll need to consult a professional coatings supplier to find out more, especially for a moist bathroom area. It's more common in high-end commercial structures such as car dealerships to see epoxy finishes rather than visible concrete since a slab must be in flawless condition to serve as a final flooring surface with a reasonably acceptable appearance. Epoxy finishes can be applied with additive flakes to help with slip resistance. However, if all you are wanting to achieve is an industrial vibe, there are so many tile choices out there that would serve you extremely well and wear better over the long haul than a visible slab or epoxy. With a skilled installer and rectified tile, grout joints can be as small as 3 mm (1/8 inch), and the large format tiles are becoming increasingly popular for homes, so the surface can have fewer lines than you might normally think about with an older tile installation. Porcelanosa and Happy Floors are two companies that have recently released new "industrial" tile collections with impressive finishes. These companies manufacture in Spain and Italy. The supplier ProSource, if there is one in your area, will have great wholesale prices on both brands as well as many others, and Porcelanosa has an annual fall sale, the last one 40% off, so you can get premium tile starting at $5 or so per square foot if you have time to shop.