About a year ago, I prepared my concrete floors to be covered first with an overlay and then stained. My situation was a bit different, but I bet the prep needs to be about the same. You can read my blog post about the preparation we did on lauramakes.com.
For your situation, you will want to use a floor scraper to remove anything loose on the floor, like paint chips and the glue, or you won't get your paint or overlay to stick well. I found that wetting down the floor made the scraping go much faster.
You will definitely need to get the carpet glue up. I was interested in non-toxic products, so I looked into two soy based strippers. I tested Soy It, and it definitely worked for paint and is supposedly good for adhesives too.
After you get up the glue, you will need to take care of the grease stains. If you don't, it may show through your paint. The Eco Safety Products support person recommended that we use a floor buffer that you can rent to clean the floor first with orange degreaser and then water. Our grease stains didn't come completely out, but I don't think we found a heavy enough buffer to rent.
I can't really answer much about etching because I decided early on that the process was too toxic for us because we would be living in the house with our pets at the same time as we were prepping the floors.
Anyhow, I hope that helps a bit and let me know if I can elaborate on anything.
The answer is "it depends" -- on what you need, on how well it's cared for, and how often you want to refinish it. Real wood is measured by something called the "Janka Hardness Scale" -- oak is a good choice, as it's rated at about 1300, with only more exotic woods being harder. I was told that Oak would probably be scratched by my dogs' claws, though, and I imagine that the invariable stones stuck in kids shoes will be worse. If it's possible, get real oak and make the kids take their grubby shoes off at the door... :-P
The "engineered" hardwoods are better because they're cheaper, but worse because they're not able to be sanded smooth and refinished. You'll usually see thicknesses plus a Janka measurement or an AC rating. The thinner the veneer, the more likely you are to crack through it no matter what the hardness of the veneer or the AC rating of the floor are.
For 100% composite stuff, such as Pergo and Kronotex, you'll see hardness measured on an "AC" scale that's basically a designation for how much traffic the wood is designed to bear in a residential or commercial setting. "AC2/Moderate Residential" will be too soft for your needs. "AC3 - Light Commercial/Heavy Residential" may be durable enough for your needs, but might show wear. "AC4/Moderate Commercial" is most likely what you'll need to go with, and it's harder to find and more expensive. However, it's less expensive than wood is no matter what.
Two things you didn't say... first, what kind of structure you're installing it on. Is it a wood subsurface, or is it slab-on-grade or slab basement? If it's on concrete in any way shape or form, you definitely want to go with something that is composite and less expensive. I know that you CAN install wood on slab-on-grade, but I would never consider doing it, personally. Second, what rooms is this going in? Wood floorings, regardless of composite or engineered or natural, is not good in places that will receive water on the surface or may be exposed to leaks. So the entry hall (front door and back), the kitchen, and the bathrooms are places to avoid having wood floors. I would keep vinyl or tile in those areas, or explore the wood-grain ceramics that are becoming quite popular for those areas or over slab-on-grade.
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As hinted at, boat coverings can be pretty tough. Spar varnish has such a reputation, and then there are the epoxy paints, which are actually probably the toughest, and most costly.