They are three entirely separate story worlds, so the order does not matter.
Avernum features a traditional 4-character party. Something to consider: There are two Avernum series now. (Three, if we include Exile.) One is the original Avernum, which is six full games plus a scenario pack. Spiderweb is in the process of remaking these. At the moment, though, only the first one or two remakes are available.
In Geneforge, you're a single summoner supported by your creations. You can name them and preserve them for the entire game, if you care to, and if you're careful. Or you can forgo any personal attachment to them and callously use them to spring traps. Also, in the Geneforges, the story always branches significantly and meaningfully.
Avadon, again, you're a single character, but you get to select from a handful of support characters (each with their own personality and commentary) depending on the mission. Personally, I much prefer the other two games. I tire of the support characters bitching at me when I don't bring them on a mission, and I don't feel very attached to any of them. I still enjoy Avadon, though.
I have no problems with the Avernum and Geneforge interfaces. Once you become familiar with them, they are fast. I find the Baldur's Gate interface (for example) downright clunky in comparison. I'd start with Avernum or Geneforge, personally.
Post edited March 18, 2014 by grimwerk