I'm confused. I've played Jagged Alliance: Deady Games II and Unfinished business and I want to play the original because it was so fun. But what is this business with deadly games? Is JA 1: deadly games an updated version of JA, or a completely different game? Is it worth getting both? And will I need to use DOSBOX to play these games?
Thanks muchly in advance :)

Deadly Games is a different game. While JA follows a storyline with you hiring mercs to slowly fight on an island, JA : DG is more of a 'one mission at a time' game without an overarching storyline. Still a lot of fun, though. DG also was the first game, I believe, with a multiplayer component (which is an absolute blast). As for DOSBOX, if it IS needed, it will be integrated in to the game's loader, so you won't have to manually do anything.

I don't think Jagged Alliance: Deadly Games II exist. These are all the JA games out there:
-Jagged Alliance (the original, one grand campaign)
-Jagged Alliance: Deadly Games (several smaller campaigns, seperate missions, a great mission and campaign editor and multiplayer!)
-Jagged Alliance 2 (true sequel, one grand campaign)
-Jagged Alliance 2: Unfinished Business (same as Deadly Games, but for JA2)
-Jagged Alliance 2: Gold Edition (Jagged Alliance 2 with the improved engine from Unfinished Business and UB itself as well)
-Jagged Alliance 2: Wildfire (a mod turned commercial. Adds a lot of stuff and makes the game harder)
All these titles are standalone, meaning you don't need one of the other titles to run a JA game. Only the first two games are made for DOS, thus needing DosBOX.