the culture cannon (I have never used it , but i've read about it in the manual, correct me if I'm being Noobsauce) is, i think, just a brodcasting center on steroids. it boosts your culture Ten-fol. great if your culture is already strong or your culture is being pushed back by enemy culture. Unfortunately, culture does not affect space pirates - they don't care about culture. The Advent are great for turtling and Winning via culture and revolting.
With the TEC Novalith Cannon, it does take two shots to destroy a non-shielded planet and possibly three shots from it to destroy a shielded planet and four for a pirate base. The TEC are all about direct fire and close-range combat. I'd suggest TEC for noobs and boomers, and because of the F'd up market dynamics, they are the most powerful faction in sins untill patch 1.4 comes out.
As for the Vasari, their Kostura cannon is actually very effective - it damages anything in orbit of the targeted planet. It does not do much damage and it will take many a shots to destroy all the orbital facilities, but it immobilizes any production on the planet AND the orbital structures for 3 minutes AND disable all ships and fleets for 10 seconds. The Vasari are quite possible the best Race for advanced playes in this game. Especially once they fix the market dynamics.
So, in the end, Cannons are very effective, and, for pirates, using the Novalith cannon to destroy the Pirate base is effective to stop pirate attacks. you could also risk an entire fleet and rush in, guns ablaze. the Idea for planetary defenses that silverace suggested is somewhat the same mathod I use, but I also add in a few frigates and later on heavy cruisers to defend those planets that would most likely be attacked by pirates.