There's no "too old" or "too new" cutoff for PS2 compatibility—it comes down to available input jacks and supported resolutions. The PS2 outputs standard-definition video (480i/480p), and almost any TV from the last 30 years can display it if you have the right cable.
Check your TV's manual (or rear panel) for input types. If it has Component, use that + 480p in PS2 settings (hold △+× on boot for progressive scan). If only HDMI, budget $20–$150 for a scaler depending on quality needs.