Pocket Internet Explorer is the Internet Explorer on your phone (PIE)
Logmein should automatically recognize your device as a mobile device. It'll ask you to install an app. Install that, and you're good to go. I use dual monitors on my PC, and when I log in, there is a button to switch monitors. I can even re-size the resolution on my Touch Pro so the PC screen shows as 640x480 (which actually looks nice).
If your phone is already on the Wifi network, you can use the HTC network plugin (google it, and you can install the app). That works great for file management. It essentially allows you to browse the shared folders on your PC, and you can pull files from your PC to your phone. Once you have installed & enabled the HTC network plugin, you would use your standard File Explorer (or Total Commander, etc...) to browse the files on your PC.
As for actually logging on to the screen of your computer, I much prefer logmein to RDC (Remote Desktop Client). RDC logs you off your PC (unless you enable dual logins while remote accessing, but again, this makes it more complicated), and sometimes resizes your PC resolution - which in turn rearranges all your desktop icons (unless you're well organized and don't have any icons on the desktop).