You will need a capture card, anything before PS4 doesn't have the processing power.
On PS4 you can stream through a PC without one.
Most common and popular are Elgato, probably cheaper ones on the market.
Not sure about TVs and monitors, I'm sure the PS2 doesn't like HDMI, maybe a converter cable if your running a newer TV.
Possibly some sort of software program depending on if your editing videos at all.
I'm not an expert and have little to no experience, but I'm sure you will need some of these things.