I slept on a waterbed for years, and ultimately realized how bad it was for my back, but there's nothing else like it so I hadn't a clue where to start.
After a lot of reading I realized a few things...
1. As stated above, manufacturers make it impossible to compare mattresses at different shops. They vary them in just slight ways along with price, so the best you can hope for is to find a very specific mattress and scour the internet for an insider who can explain what is what, but you'll likely fail.
2. I gravitated toward foam beds... they seemed to offer the most even support and that was important as I had developed some back issues. And then I had to dig in to the variations on that.
a) Memory Foam. Everyone knows about Tempurpedic memory foam, but it's not cheap and I saw lots of complaints that memory foam sleeps hot. There are variations out there where they introduce gel into the foam to combat this, so they keep introducing new mattresses. Then there is the cheap poly foam, and Latex.
b) Latex is an interesting topic all on its own.. it does not sleep hot, and it can last 30 years which is much longer than the traditional mattress that winds up losing support in single digit years. Latex is also popular with the naturalist crowd because it comes from a 100% renewable source, and it is ideal for allergy sufferers, doesn't outgas like memory foam, and doesn't harbor microbes like a standard mattress. You can also get man made Latex which is cheaper, but from not as renewable sources, and honestly it started to become difficult understanding the idiosyncrasies of Latex manufacturing. Most interesting is that base latex is firm... and very popular with those with back issues, but with various molds they can make them less and less firm. Base/firm Latex is fairly affordable.
3. Layers. All mattresses are composed of layers, and this is what makes shopping so difficult even if you decide on the base component. Even spring mattresses have started to incorporate the various types of foam in their layers, so you can claim "memory foam" but let's be honest, 1" of memory foam is not going to do anything for you. I still don't understand how 1/8" of memory foam does anything useful in shoes, but I digress. Then there's cotton, wool, springs, and a million other possibilities.
So trying to cut this short, I found an all Latex mattress at Macy's by Sterns & Foster based on internet advice. With various discounts I got a really good deal, particularly since they don't need a box spring so that was added savings. In hindsight that was a load of crap. Latex lasts 30 years, but within 4 years that thing was no longer supportive, so it was probably a poly foam with a thin latext topper. poly doesn't last all that long, but plenty of people us it... it's probably cheap enough to replace every year compared to standard mattress prices. The warranty for the S&RF required a 3" indentation before replacement but it was closer to 2". When I moved I tossed that mattress.
With all that hard knowledge acquired to date I took a winger on a mail order Casper mattress. I was tired of being confused at mattress stores and their high prices, and the composition and layers looked fairly ideal. It turned out to be very comfortable except that being a side sleeper I would get aches in my shoulder because I would sink right through the softer top layer and hit the harder base foam layer. Yes, mattress choices also vary based on how you sleep too. Casper has an excellent return policy, but they talked me out of it by sending me a latex topper, which mostly did the trick. So now I have the advantage of cooler softer Latex on top and enough support. That was a first run mattress, and I believe they have made some changes, but here it is 4.5 years later and it still does fine.
I still wouldn't consider the mattress 100% ideal though... in fact I still don't know how to answer the "what is ideal" question but I have a hunch. Next time I'll be more specific on the layers, paying attention to the densities and thicknesses of each. I think deeper mid-firmness layer would have helped me from hitting the base but a soft topper is still recommended. Casper is close to that but again not perfect. There are mattress firms where you can specify all that, even varying it on each side! Now there are other mail-order competitors, and it comes down to the simple fact that the whole process is very personal, and very trial and error.
Just remember you spend 1/3 of your life in bed, so that's one of the few things worth the extra time and money. Both mattresses were around $1k, so neither was a big investment, but they can easily climb to 5x that. I hope this was somewhat helpful.