What ps1 games backwards compatibility is power rangers light speed rescue and tomb raider2 ps1 ps3?

Any PS3 model should be capable of playing PS1 discs with a fairly high degree of accuracy. The only issues you'll likely run into are that you obviously can't plug any special accessories into the PS3 such as a GunCon or Multi-tap.

PS2 discs are only playable on the earliest PS3 models but PS1 works fine through emulation.

Ps3 runs ps1 games through extremely accurate emulation. Every game is technically supported, so it should run those games fine, with possibly some minor frame skipping or very minor emulation issues. The tomb raider games all run near perfect since sony actually re sells them on psn. The power rangers game should be fine... Although honestly your better off downloading a psx emulator for pc or mac (or android or a raspberry pi or similar device)  and play the games off there since you will get additional resolution and graphics enhancements as well as save slots and etc.. 

All PS2 consoles could play all PS1 games.

Because the PS3 launched with very few games, Sony equipped the very earliest PS3 consoles with internal fully-functional PS2 circuitry. They’re recognisable as they’re the only PS3 to have four USB sockets on the front instead of just two.

But those early PS3 units are now very hard to find in good working order at sensible prices. 

Just buy a PS2 console instead; still easily available and very cheap. But unless you buy from a reputable source which gives warranties all PS2s are now old enough that they may be worn out or in need of repairs. So don’t buy privately unless dirt cheap and you accepting the risk, or unless you can try before you buy, but with CV19 few sellers can offer that option.