I'm using the downloaded version of HL2, E2. I find I am able to scroll through my weapons inventory BUT the last weapon highlighted is not selected. I can find no way to change weapons. I can't even re-install the game because it was downloaded. This is the last time I do that.
Check out strangestranger's post because fast switching is definitely the way to go for you.
Is there no online help available with HL2 or HL2 EP2 or isnt that the real problem that is bothering you? Are you the type that actually reads the manual that comes with a retailbox or are you just picking on Steam for fun? (by all means go ahead but this weapon selection is something that you could have figured out for yourself easily, however I sympathise with people that actually read manuals so that they can enjoy a game fully).