The only real backwards compatible is the 60 GB one. That model is the only one that works on hardware instead of software, so its almost 100% compatible. However, it has been discontinued for years and it might be difficult to find.
The other option is the 20 GB and 80 GB ones... Those use software emulation, so it doesn't always work and even when it does its not 100% perfect.
So, yes. The only reliable way to play ps2 games is with a ps2. Might sound stupid, but its Sony's way of making that console still relevant.