I recently got Reassembly and am kind of pissed when the station I spawn at it surrounded by nothing but farmers and their point defense and shields (Because the autocannons and missiles can't do shit to their shields).

Missiles do little/no damage to shields, but autocannons and other "gun type" weapons work perfectly fine against them, you just have to remember that larger shields regenerate any damage taken (while still active) pretty fast so you'll have to put a decent amount of damage into them in order to bring them down.

Farmers are generally considered one of the easiest factions to beat, their shields are mid-tier at best, but their hull is pretty weak, their guns are not tremendously powerful and they have pretty weak thrusters.

Also, from the sounds of things you might only be using one or two of each weapon, don't be afraid to modify your ship to have lots more, with say 4 missile launchers most smaller ships will have a very hard time stopping all the shots from getting through.