How big is the lake, do you need to cast long distances?
If the answer is no to the above then I'd be on 15lb, 18lb or 20lb mainline (though you should still be able to cast a fair way with either breaking strain line). You should be looking at a mainline that is known for being abrasion resistant especially with the presence of lily's, reed beds and tree over hangs etc as the carp will want to get into these if you hook them.
Hooklinks are personal choices and should really be determined by what the lake bed is like, gravel, silt, clay etc, suit your hooklink to whichever you're fishing over. As for the breaking strain, most are between 15lb to 25lb I'd say and once again with the lily's etc I'd go on the heavier side personally.