I'd like to be able to activate items (ideally) with the keyboard numbers, but 1-6 are reserved for unit groups, correct? I assume those cannot be assigned to items.
Update as of 18/1/2013
The options menu has been changed to make it easier to find the control rebinding for items. I have taken a new screenshot - simply click on steps 1 through 4 from anywhere in the game client to open up the menu and rebind your item hotkeys.
Note: this part of the answer is outdated, but I left it alone for now. If it's appropriate to delete it, mods are welcome to do so.
You can change the key bindings for both abilities and items by clicking their icons underneath the list of controls in the options menu. Below is a screenshot of the controls menu, you can see that I reassigned my items to numbers 1-4 and my extra mouse buttons.
It is not immediately apparent that these buttons which look like the ingame HUD are actually additional key binding options, but each one that is labelled can be changed.
It's also highly recommended that you rebind at least a few control group keys to something else, but it's rare that you will need all 6 control groups in a normal game. I chose F1-F3, but you can use whatever you like.
Hit the gear button (Options) in the top left corner of the main menu. From there, you can edit/re-bind all the keys, including 1-6 which are by default for unit groups as you've said.