I shoot about 18,000 rounds of trap a year and here's what I do:
After each shoot I'll run a bore snake down the barrels with just a touch of oil. About once a month I'll scrub the barrel with a brass brush and Shooter Choice. I shoot reloads and use Claydot powder as it's very clean burning. If I'm using factory stuff I'll clean it just a little more often. Unless you shoot thousands of rounds plastic build up isn't a big problem, you may find it inside your choke tubes and they clean up easily.
The BIG thing to remember is after every shoot loosen and retighten your choke tubes and when you scrub your bore remove the tubes, clean the threads real good, lube them with a good choke tube grease and put them back in. I've had problems with two of my Browning forgetting to do this, both guns had to be sent in to get the tubes out.
Don't worry about the porting holes, you can clean them with a pipe cleaner if you want, but I just wipe them down on the inside and outside.