I'm not 100% sure, as I've never actually owned a PS3 myself, but for the backwards compatibility question, I believe the backwards compatibility was limited only to PS2 games, not PS1. I could be mistaken though, since as I said, I've never owned one... (Never had much interest in the system or its games...)
Actually, all Playstation consoles will play most Playstation 1 games. The only machines that are not fully backwards compatible are the Playstation 3s other than the 60g. The 80g version will play some PS2 games, but not all due to the fact that the 60g basically have a PS2 built in, and the 80g uses software to emulate a PS2. No other models will play PS2 games.
However, all PS2s and PS3s play PS1 games.
In a move that is rather NCSoft-esque, Sony originally planned for the PS3 to be backwards compatible, but when the system first game out, the PS3 games were still competing with the PS2 ones. So, in order to make their game developers happy and to try to force the players to move on, they removed the backwards compatibility. To their surprise, this did not alieve the situation, but actually made the sale of PS2s go back up.
What they didn't realize that the PS2 was still an extremely viable system and that it would be years before developers made games that could actually show a real difference between the two systems. But, even now the 2 is still a great system and, if companies were allowed to, could still make games for the system that could compete in today's market.
That beings said, finding a working system from the store or ebay will still cost you a good 60 bucks, and the games are still usually around 5 dollars used. Of course there are the expensive titles like the Fatal Frame series which, depending on the condition, can cost you nearly 100+ bucks for the first three games. 200+ if their not opened.
As for your other questions, I'm really not sure, but for the large part because of how much technology has changed over the last two decades, you're probably going to need one of the older TVs/Game systems to be able to play them properly.
I've resigned myself to that fact, but it doesn't bother me. Cathode tube TVs are fairly cheap.
I'm not sure on prices for old PS1s and PS2s as I've seen wide price discrepancies depending on where you look...
You can find the PS1 for just about any price. In your local Salvation Army or Goodwill store for 15 bucks, from a friend for 5, or for $20 and up from electronics stores and pawn shops. The things never died and were incredible machines for the day. They will likely be around forever. I found a really nice deal on eBay for two PS1 consoles, 5 regular Sony controllers, 3 different light guns, a fishing game controller, a hand full of memory cards, and 9 games. All for under $100.
I didn't know that the older light guns didn't work with the newer TVs... Definitely something I hadn't thought about, probably because I havn't played a light gun game since Duck Hunt on the original Nintendo Entertainment System when I was 5...
You're about my age then. You may find this interesting. The Zapper (old NES gun) was fairly simple in how it worked. When you pulled the trigger, it made the screen go black for a frame, then the targets would turn each turn white for a frame, one after the other, and then the normal screen would come back. The gun would tell the system weather or not it hit a target and when the target showed up, that way the system would know which target you were pointing at. The whole process was around a second long. Pretty impressive for the 70s and 80s. In fact, the technology is as old as 1969, when they came out with the light pen.
The "Super Scope," Nintendo's second gun, worked like the guns in the arcades still do. Pulling the trigger still makes the screen flash, but this time it uses precise timing of the electron beam and how fast it travels through all the little pixels in the screen, one by one. The gun sees exactly when the beam passes through the pixel at which you are aiming and tells the system. It's impressively accurate.
However, since DLPs, LCDs, and plasmas don't use cathode rays and phosphor pixels, the old guns don't work, and you need to buy the newer guns which require to place sensing strips on either side of your screen.
If there is a way to get the GunCon 2 (the Namco gun for the PS2) to work with the PS3, I'll be good to go after buying a cheap used TV. My luck, though, I may simply have to buy another PS2.