Definately Mort next - although it's book 4, nothing in book 3 has an impact on the things happening in book 3.
If your other books haven't arrived when you've finished with Mort, I'd say your pretty safe with Reaper Man (which is among many a fan's favorite books). After that, Soul Music, then Hogfather, then Thief of Time - these books all deal with Death in big parts. Still, I'd recommend reading those already ONLY if you haven't received the books inbetween yet.
For the others:
Don't read Feet of Clay, Jingo or Thud yet. These books are about the watchmen of Ankh-Morpork, and best read in order.
You seem to enjoy Rincewind, so try and get Sourcery soon. It picks up where Light Fantastic ends. Rincewind's adventures continue in Eric, and in Interesting Times after that. You might have overdosed on Rincewind by then though
Monstrous Regiment seems a standalone book, but there are many, many (short) appearances of characters from other books in there. I think you'll very much enjoy it without reading the previous books, but you'll miss out on lots of stuff.
Once again, I usually recommend reading them in the order they were published. You see the Discworld and characters evolving that way.