(EDIT: Dammit, SJ beat me to the answer)
We had a whole thread devoted to ship/training facilities; the general consensus was that using them in a single-player vs. AI game is almost like cheating, since the AI doesn't use them. So the answer to your question is yes, the training facilities are useful; a ship with 20% experience gets a +20 modifier to attack and a +20 to defense (which means 20% greater chance of hitting the other guy, and a 20% greater chance that the enemy will MISS). If you use both types of training facility, and send out a fully-trained fleet with fully-trained ships, the ship and fleet experience combine to create 40% bonuses for attack and defense. Considering that it's VERY difficult to increase fleet experience without the training facility, this is a MAJOR bonus.
I tend to ignore the Neural Net, partly because it's so big and partly because it would really need to be on every ship to offer an advantage. Although I guess it would be a nice trick to train a single ship (in a one-ship fleet, of course) while building lots of other ships, each with a Neural Net. Then, when you fleet the new ships with the trained ship, you have the effect of a fully trained fleet without having to keep all those ships over the training facilities.
Not certain what you mean by the computer tech enhancements for ships; if you mean Master Computers, they add a fair amount of expense to smaller ships, but since they replace the Bridge/CQ/LS components, you can save a lot of space, particularly on the larger ships; and on the largest ships (Baseship, Battle Station, Starbase) you can actually SAVE money, as the Master Computer is cheaper than a Bridge + 4 CQ + 4 LS components. The Master Computer is also immune to the Psychic weapon Allegiance Converter; this is supposed to be balanced by the Master Computer being vulnerable to the Computer Virus weapon, but the AI's don't use computer viruses (nor do they use the Master Computers).
If, by computer tech enhancements, you mean the robotoid factories, computer complexes, and databank complexes, they are also quite useful, if used properly. Since they give up to a 30% production bonus, as long as you have 4 or more of a particular facility affected by the bonus (for instance, 4 mineral miner facilities on a planet, plus a Robotoid Factory), the bonus will generate more than a single facility could. Also note that facilities affecting a single planet do not "stack", so a Robotoid Factory plus a Mineral Scanner will only provide bonus from one of those two facilities (whichever bonus is higher). System bonuses DO stack with planetary bonuses, but again you can only have one facility providing a particular bonus per system.
I hope that's clear enough - I kinda started rambling near the end. But I'm sure many others will also post answers here...
[ July 31, 2002, 20:16: Message edited by: DirectorTsaarx ]