Jeff,
I ran several TCS campaigns, some concurrently, during various operational deployments while in the Navy. This was in the early to mid 80s so no personal computers were used either.
Take it form me, TCS is a record keeping nightmare, especially for the GM/referee who must have copies of EVERYTHING the players have. Computers will make this easier; I've seen a TCS starter kit of sorts complete with ship designs on line in some sort of MS database format.
Early on, the battles are die rolling - record keeping headaches, especially if you don't limit the number of pilots somehow. The HG2 weapon tables create optimal design solutions at every given TL. Most of those solution favor smaller hulls over 'deathstars' thus requiring more pilots. ForEx: Before powerplants reach a certain power density, nuc missiles are your best bet. That means most naval budgets will have HORDES of missile boats carried by armored tenders. (Even the much maligned sub-100dTon fighter is a ship killer below a certain TL, ~12 IIRC.)
I ran all the campaigns like 'Strat-o-matic' baseball tournies. The players were responsible for two sets of orders per week. They could either fight the battles against each other or have the referee crew fight them according to simple instructions; i.e. break off after X amount of damage, refuse to engage if Y occurs, etc.
For most of the battles we used the statistical battery resolution rules published in JTAS. That let us handle the huge numbers of 'to hit' and 'to penetrate' rolls huge numbers of batteries required. Rolling for 100 laser batteries per each battleship will break your wrist.
As much of a record keeping nightmare as TCS is, you'll be glad that certain things like supply and planetary assaults are either ignored or handled by simple/simplistic rules.
One result I did notice over the course of many games is that new builds; ships laid down after the war begins, rarely proved useful. TL 'leeching'; you take and hold a port with a higher TL than yours long enough to build there, NEVER happened either. Most wars were fought with what the parties brought with them. While repairs mattered, new builds and new tech did not.
Counterpunchers seemed to fair better in many games. There were laways those fellows who would open the game with an all or nothing assualt on a rival. It made for a huge battle and lots of scrap iron. It also usually failed because most folks had monitors in their OOB. (You must build a certain percentage of your budget at TL-1, monitors are a nice way to meet that requirement.) The death or glory boys would always prove easy meat for the counterpunchers.
Many players struck on the idea of hi-gee, double jump, heavily armored 'scouts'. They'd jump into a system and immediately break off from combat by either acceleration or jump after getting a peek at the opposition. (Remember, at long range all you know is the rough size and actual number of ships. However, you can ferret out just what is what after you engage in a few battles.)
Hope all this helps. You're in for a lot of work and a lot of fun!
Have fun,
Bill