Howdy yutterh,
Welcome to the fascinating world of Alpha Centauri!
First, did you get the game through GOG or from some other source? I'm asking to make sure that you have the most recent patches.
Here are some threads that contain advice for newcomers:
http://forums.civfanatics.com/showthread.php?t=480362
http://forums.civfanatics.com/showthread.php?t=413510
http://forums.civfanatics.com/showthread.php?t=458030
http://forums.civfanatics.com/showthread.php?t=434901
Read these over and see if you have any questions.
Many players like the University because of their inherent tech advantage, but they do get more drones than other factions. However, drones are part of the game, so you might as well learn how to deal with them. Playing as the University, you should prioritize building the Virtual World Secret Project. That makes all your Network Nodes (which each base automatically receives) act as Hologram Theaters, supressing two more drones.
If you're having problems with early expansion, perhaps you're building too many scouts and formers. In the early part of the game, you only need one former per base, one garrison unit to defend the base and one or two other scouts to explore your territory. Other than that, your bases should be building Colony Pods to found new bases.
You said that you're running the two Social Engineering choices that aid growth, which I assume are Democracy and Planned. Planned is a good early choice since it increases growth and industry (build things faster). The negative efficiency from Planned doesn't hurt you until slightly later in the game. However, you should hold off on adopting Democracy until after you've finished with your base expansion. The reason is that when you adopt Democracy, new bases lose the 10 free minerals that they would otherwise get. It then takes longer to build your first unit and slows down the initial development of your bases. Also, as you observed, the negative support is more difficult to deal with early in the game.
You mentioned a strategy guide. Which one are you referring to? CGN's
SMAC Academy contains many useful articles. Alphacentauri2 has a copy of
Vel's Guide, which is a rich source of information.
So, I think that's enough information to help you get going. Please feel free to ask more questions!
Petek