I regularly play SoaSE but one thing that I haven't found is a good explanation/tutorial of the differences between the weapons present in the game and their effect on the hull and shield points of the enemy ships.
Any good pointers?
Any good explanation of the different weapons and their effect on Sins of a Solar Empire
sins-of-a-solar-empire
Related Solutions
You can either change the language file or install it through Impulse. Take a look on this thread on the official Sins' forum.
You'll need the anti-structure cruiser, introduced in Entrenchment, which acts as hard counters to Starbases and other defensive structures. The TEC's is the Ogrov Torpedo Cruiser, which is basically a giant moving missile platform that is ridiculously good against structures (including Starbases) and nothing else.
The Starbase you were facing appears to be very well upgraded, which means that you need a good number of these, plus a fleet to protect these against any other ships in the gravity well since they can't defend themselves.
Best Answer
If you Google Sins of a Solar Empire wiki there a quite a few fan made wikis that could hold the information you seek.
Update: Found this google spreadsheet. Probably as good as you are going to get.