1920x1080 is the best resolution to get. 720/1080p content should display fullscreen fine (x360, ps3), pc runs fine at that resolution, not sure what the wii resolution is but most likely it will run fullscreen fine as well. due to the age of the ps2 and the type of monitors/tvs available at the time it will probably display in a square (4:3 ratio i think) box on any monitor you get. there will be black boxes on the left and right where the monitor isnt being used (but only for the ps2)
you could probably convert all the cables to hdmi and go with an hdmi switch if that is the route you wanted to take. ps2 has component video outputs and they make a conversion to hdmi from that.
The whole idea behind my setup is to share one tv and one set of speakers with all my components (2 for now, but much expansion capability).
i have my pc and my ps3 hooked up to an a/v reciever which in turn is hooked up to my 5.1 system and my tv. changing inputs is as simple as turning a knob.
granted, going this route will most likely cost more (even if you get cheaper equipment) but i've found it to be a great way to link all of my media equipment together. on the plus side you can use home theatre speakers and subs instead of the often inadequate pc speakers.