If you want it to be keyboard driven then your best bet is to create a new menu on the menu bar (or add to an existing one) and put the Go-DriveButtons command in it. This will turn into a list of drives, and it has options to filter by type or drive letters, as well as to display icons or different kinds of labels.
If you put an & before one of the letters in the menu's name you can pop it open using Alt and the menu's letter.
Have a look at the Toolbar editing video tutorial for an easy way to see how to set up the Go-DriveButtons command and to get a handle on toolbar/menu editing in general.
It's also possible to create a menu which pops up from other hotkeys (e.g. Alt-F1 as you mention) and isn't part of the menu bar or a toolbar. At the moment, though, the problem with doing this, in combination with commands like Go-DriveButtons which generate a list automatically, is that the menu will stay open after you select a drive.