LCD's dont rely on refresh rates in the way that old CRT technology does, the maximum refresh rate is the same as all other LCD's.
As for the resolution. It is 1366x768. so it is true HD-Ready.
If you want higher resolution for PC then you need to be looking at LCD monitors rather than LCD TV's like the Dell 2405 you mentioned originally. But bare in mind that the output of the the xbox 360 is 720p in HD mode so 1366x768 is more than enough. Anything higher and the monitor will have to do a lot more scaling and the picture will arguably be worse depending on how well the monitor handles such scaling.
I would personally go the LCD TV route since you plan on hooking up two consoles as well as a PC to it, and as far as I know the LG is one of the best (if not the best) LCD TV for PC use.
I'll explain a bit about the difference between LCD TV's and Monitors...
LCD Monitors are designed primarily for PC's and as such they offer very high resolutions.
LCD TV's (the new HD ready ones) are designed to play back high-definition content from DVD's, consoles and whatever else. 720p HD content is displayed at a resolution of 1280x720. The TV's themselves generally come with either a 1280x720 or 1366x768 native res and slightly scale the image to fit. An LCD monitor will obviously have to scale the image more since it has a higher native resolution.
If you wanted a TV just for Xbox 360 output then any LCD TV offering a res of 1280x720 would be perfect. But some of these TV's are not too good with PC output. Therefore your options are either an LCD Monitor which is designed for PC and should do reasonably well on consoles, or an LCD TV which offers 1:1 pixel mapping (which basically means the output from a PC will look perfect with no need for scaling). By Going the LCD TV route you get the best of both worlds and will get a far larger screen for your money. But you will have a lower resolution for PC usage than an LCD monitor like the Dell 2405.
It all depends on what you plan to be using it for most often. If the display is going to be primarily used as a PC display get an LCD Monitor. If it is mainly for the Consoles get an LCD TV. Or if you want the best of both worlds and dont mind having a slightly lower resolution for your PC usage get a 1:1 Pixel mapping LCD TV like the LG 26LX2R.
Hope that helps a little matey!