[Will]

I've actually found that fighters can be very useful, even when tech is high. But you have to build lots of them. As in, every single planet you have that's not building facilities or ships, are building fighters (or troops). I had a bunch of movement 2 carriers that only sat on warp points to ferry Groups of 100 fighters to the next system, and transports. Transports were generally used to collect fighters at a single planet for launch, as the fighters are faster than any other ship. "Conquest" fleets would have a faster Version of the ferry carriers, which would split from the fleet, go into the system to be attacked, and launch fighters. The fighters would beeline to all the warps, sealing them off (when you have a single stack of about 100 fighters with Electric Discharge III, there are very, very few ships that will survive a single shot, so it would take a very big fleet to break through). Then small Groups of ships will go in and kill any stray ships, while the main fleet will attack the largest planet, and capture it. That planet immediately starts producing troops to help capture the rest of the system. Very effective when done right.

Anyway, as for your problem... Probably the best fighters are ones with Electric Discharge or Time Distortion Burst (the latter especially with heavy-shielded enemies). If you want to take them out with fighters, I don't quite know what "standard" weapon would work best, but you'll need a lot of them. Your best bet, though, is to have the PDC boats mentioned. Make them as fast as possible, size should be in the Light Cruiser to Battle Cruiser range. Experiment with the ratio of PDC/Armor/Shields, find the best combo.