I always thought that X-Com is actually a fairly simple game, most stuff doesn't matter and you don't use a lot of features at once. It just gets complex once you actually start getting deep into it strategizing and figuring out all the best/worst stuff and etc.
The main problems is on a first play, players have no clue where to start, and asking us veterans will just get them a barrage of excessive info telling them exactly what to do and not do (eg. Ufopaedia.org), and sucking all the fun out of it.
On that regard, I think the manual was great. It had tutorials for the key elements of the game to get players interested, making sure everything had a logic following and solid foundation before going deeper, but of course nobody's gonna look at it anymore.
So here's what I'd suggest:
Tutorial 1: Shooting down your first UFO (Geoscape)- 50% of the game is waiting for UFOs to shoot down and raid, so a good starting point.
- Don't get into all the boring micromanagement stuff yet, get them into the action and fun stuff.
- Key elements: time controls, interceptions, crafts, countries.
Tutorial 2: Killing those alien bastards (Battlescape)- 50% of the game is killing aliens! Get them into the action and used to the bullshit.
- Follows up from getting your first crashed/landed UFO.
- Key elements: turn-based, equipment, actions, camera control, mission win/loss.
Tutorial 3: Base management- Follows up from the first mission, they'll want to know how to prepare for the next one.
- Hopefully you got them hooked now! So they'll learn even the boring management stuff.
- Key elements: equip craft, purchase/sell, facilities, research/manufacture.
Tutorial 4: The end-game?- Where to now? Scoring, funding, goals.
- Maybe get deeper into stuff like country coverage, base building, soldier stats, etc.