My experience:
I had never played a single board game until a couple of years ago, when a couple of friends showed me The Lord of the Rings LCG, and a few others. Right now they seem to be undergoing a massive upswing in popularity. I thought they looked horrifically complex. But actually, once you have seen someone else with experience play one, you can play anything - most of the time, they are having to dip into manuals and stuff, to ask questions as they go along - so don't be intimidated by the absurd complexity some seem to have.
There are now, finally, solid Star Trek games coming out, like
Star Trek: Fleet Captains:
Most board games tend to have little or nothing to do with the setting they depict, and don't accurately model it at all - take
Star Trek: Catan for example - it's just a lame re-skin of a board game about people moving across land on wagon trains. Take Star Wars: X-Wing or it's clone
Star Trek: Attack Wing as another example - this time it models the setting, but only one minor aspect - combat; making it boring and unworthy. But in the last couple of years, a couple of companies, such as Fantasy Flight Games and WizKids, have been producing really solid adult and thematically accurate games. Some have been Star Wars or Tolkien, but recently the Star Trek license has started to be used with the same degree of seriousness and consideration - the games coming out now are no longer just gimmicky tat:
Star Trek: Fleet Captains is a rock solid game that models the exploration of space by a small fleet
Star Trek: Ascendancy is an upcoming game that seems to be like Birth of the Federation
Star Trek: Frontiers is an upcoming game that where you actually lay down new tiles as you explore
So right now, the only one that's part of this modern wave is Star Trek: Fleet Captains - and it's good, and re-playable - and it has good miniatures and decent card quality (which adds a lot to any tabletop game, I can tell you) - but I expect that this year, we are about to get two very strong contenders.
WizKids is starting to use the license properly. Soon we will have Trek games that are the same quality as House on Haunted Hill, The Lord of the Rings LCG, the Battlestar Galactica Boardgame, the various Star Wars stuff, etc. And what anyone will tell you is that these games are 100 times more enjoyable if you enjoy the setting - so a Trek game of this quality would be the best thing ever, since the setting is startlingly interesting. Fleet Captains for example models missions, landing parties, combat and exploration. That's already a pretty solid chunk of what makes Trek what it is. The Battlestar board game is an example of a non-Trek one that works and feels exceedingly accurate - you play as any BSG character, and one person is secretly a Cylon - it feels just like seasons 1 and 2 of BSG. Thats the kind of thing I'm looking forward to from a Trek game.
Just bear in mind the number of players - if you are gonna have trouble getting friends to play - I think Frontiers and Ascendancy might be solo-able, but Fleet Captains ain't - and it is hard to play if say, you have 5 friends round, or another odd number.
Star Trek: Expiditions is solo-able, but it seems to be something you can only really play once before you have seen it all.
We could easily have this forum providing support and stuff like boardgamegeek.com. If anyone needed any advice on rules, like regularly gets posted there - I, for example, might be able to help, having played three games of Fleet Captains. What tends to happen, is at a geeky session, people will always be getting on their smartphones on boardgamegeek to ask about any rules that are unclear.
As for RPGs, Trek is sort of unsuited, as it's an ensemble genre.
And wargames like Warhammer 40,000 also don't suit it for obvious reasons, so
Star Trek: Attack Wing really doesn't seem worth it to me - just a cheap cash in on the Star Wars: X-Wing game, which is itself boring. You need more than that.