Generally speaking, for mid-game TEC you want your fleet supply to be 1-3 research levels higher than your capital ship crews. The TEC faction really should be clinging to the notion of fewer higher level capital ships.
Now, it would be nice if you told us what is killing your units. How many frigates does the enemy have, and of what type? What defenses is he employing? It does sound to me like a starbase is the culprit; a small fleet like the one you describe wouldn't stand a chance against a heavily upgraded base. If this is a Vasari enemy, you're outta luck and you'll need a much larger fleet to plough through it. If it's a TEC or Advent starbase, just set your units to "hold ground" behavior and keep your distance; you can easily kill the starbase with bombers or Ogrovs and it's largely helpless against these attacks.
For units, you need to try and get the best balance of survivability and damage. Upgrades are nice, but you generally want to focus on numbers first. With only 40 LRM's, you really don't have any business with more than the first tier of upgrades, and you'd be much better served by building additional numbers. Remember, the higher-level upgrades are balanced around huge fleets (like 1400+ command), so they're ridiculously overpriced for smaller fleets like your own.
Early to mid-game, you can get away with a nice mix of Javelis LRM (about 70%), Garda Flak (about 10%) and Hoshiko Robotics (about 20%). Vary the proportions according to the kinds of units you encounter. Throw in a few scout frigates into the mix to reveal mines and "look before you leap" and this simple combo can carry you into the late-game with sheer cost-effectiveness.
Generally you either want to transition quickly (skipping damage upgrades) into the Kodiak or slowly into the bomber as time goes on. The Javelis remains a powerful unit, but upgrading to higher-level units is a good idea as you progress. Armour and hull is always your top research picks for TEC; they give you by far the best value of any of your upgrades.