Techromancer: About the only shield enhancement I ever use is "Hard Shields," though that's mostly if I figure on running into Transporters. It's rather handy inside a Nebula as well.
For the most part, the specials I tend to use are basic ones - Battle Pods, ECM, Reinforced Hull, Battle Scanners (for beam ships and scouts), Augmented Engines. I'll make use of Warp Dissipaters if I can get them (I always research Planetary Radiation Shields) - those go either on Titans or on dedicated destroyers which are otherwise equipped only with defensive systems and PD guns.
I seem to use different things for different jobs.Most of my ships Battleship and larger start with Battle Pods, ECM Jammer and Reinforced Hull. When I get more room, I add some specialties. On the Gyro battleship, I will add Augumented engines and sometimes Heavy Armor if I have it.
I use a titan for the heavy beam ship with my best beam weapon (HV). I add to the basic three the Rangemaster and the Structural Analyzer (if I have it) Later in the game, I sometimes add the high energy focus, but I don't research it.
If I am luck enough to get the Black Hole from Orion, I will add to the basic three a Subspace teleporter, Augmented engines and Heavy Armor