I just downloaded SQ 1 - 3 and am trying to play SQ1. I can move Roger around using the arrow keys, but how do I get the mouse cursor/action icons to appear on-screen?

You can't use the mouse with SQ1 via DosBox. The game was originally created to only work with keyboard. However, you can run the game through ScummVM and have mouse support. However it doesn't really work all that well

The EGA version of SQ1 doesn't have mouse support, but someone did make a browser-based version of the game which allows you to use the mouse:

http://sarien.net/spacequest

I believe the Mac version did have mouse support.