My monitor doesn't support VGA
Just RCA/Composite, RGB/Component and S-Video
View attachment 26970
From that selection i would go with RGB (with the 5 RCA connectors), is the most standard, good quality and future proof
In my oppinion, the ideal cable is the photo posted by jolek
If you find a cable like that it will be perfect, and is way better than using several cables connected to each other, keep in mind everytime we connect a cable to other cable there is an small quality loss because the connectors itself, just to show an example... the second option is better:
AV connector (PS2) ---> to SCART ---> to RGB (TV)
AV connector (PS2)---> to RGB (TV)
But dont spend 39$ in it dude, thats a lot, i dont know how much they cost but i would pay 10$ as much (unless you find the official ones made by sony with metal RCA connectors and "fireworks", this ones should be a bit more expensive)
And btw, when looking for them you can search for PS3 video cables, as mentioned before the AV connector of the PS2 and the PS3 are the same, so the cables are the same, but probably is going to be easyer to find sellers announcing cables for PS3 than PS2
Edit:
The "problem" of the BNC connectors of your TV could be solved by buying 3 of those (BNC to RCA adapters):