360 can display all 360 games in any HD resolution. Since your TV can support both 720P/1080I, mess around with the 360's settings to see which one looks better. From my experience, 1080I tend to look a little bit better with 720P TVs. The 1080I siginal just looks a little crisper.
The PS3 strangely is much more limited in what resolutions its games can be displayed in despite being touted as the only "True HD" console. The HDMI automatically detected what resolutions my TV were capable of but it might be different for you. You can also use the PS2's component cables like I mentioned yesterday. With the PS3, most games would be displayed in 720P but there're several that will support 1080I/1080P. The PS3 can scale with a software method or just natively render in 1080. Since most 1080 natively rendered games have terrible framerates and the software upscaling is pretty lousy, I would just keep the PS3 at 720P to avoid headache.
With the PS2, things are a little bit different. You have to go to game settings to set the upscaling options. With the PS2, everything can be upscaled to the HD resolution that you selected in Display Settings. You can select upscaling to off, normal, or Full. Normal works most of the time but use Full if the scaling makes the picture too small. Also, keep in mind that no upscaling is used if you turn on Progressive Scan within a PS2 game. Native 480P rendering will usually look better than upscaling to HD.
The WII looks quite a bit better with component cables, regradless of whether you use 480I/P. I think it's worth the $30. WII's graphics are not great, obviously, but they're not worse than PS2 or PSP. So if you can tolerate playing PS2 games on your HDTV, I see no reason to not hook up the WII also.