Ive been fishing a river recently and have mananged 3 carp to 22lb.
If there are marginal shelves stick to finishing at the bottom of these. If there isnt obviously find your depths, different contours, and bankside vegetation/features.
On the rig front i tend to use either 8 or 12" hooklinks with a 1.5-2" hair with a double 14mm or a mix of 18mm and 16mm double bait i do this purely to avoid the bream. Keep things simple i.e. supple or mono hook lengths (imperative to have a supple hair because it ensures the bait leaves the carps mouth before the hook), inline lead (enough to hold down in the current), no leader and use a backlead but make sure the backlead is at the bottom of the near marginal shelf to ensure your line isnt zipping mid water through the river and fish tight lines.
Bait, i would purely go for fishmeal boilies as ive found more of the silver fish home in on the particles and pellets, however i would use a combination of hemp and boilies and mainly use the hemp to regularly bait swims to get any local carp constantly visiting that are, and as ive stated about double baits this ensures your chances are lessened to hooking any nuisance fish. Also if you introduce any baits try and ensure the bait goes in when hours of boat traffic are at a minimum as with the flow of water+boats your baits will merely roll and flow downstream with the current and ive found the carp seem to feed more from 11pm-10.30am (from my captures and other members of the club) simply because boats traffic is at its least (less commotion and disturbance).
As for the carp themselves and there grouping/pods ive found they seem to be very nomadic always moving on the search of a free meal and tend to swim in pods of 3's.
Id hit these shallow margins that you mentioned in the summer when the thermocline has changed and the temperatures high in the water column as the carp will be further up the shelf due to the warm temp. exciting there behaviour, how ever dont ignore the bottom of the shelves (both near and far margins) in these hot seasons as the bottom of the shelf is where all the food is gathering after falling off trees/bushes and rolling down to the bed.
Here are the fish ive had...
10lb 2oz......1st carp (5am)
7lb 2oz.......2nd carp(9am)
22........3rd carp it may not look 22lb but it was as chunky as anything, just pure solid muscle(4.30am)
The 22 has probably got to me my most memorable catch from the river i woke up to 3 frozen alarms, the middle hanger had came of line which i thought was a violent knock from a bream so i clipped it back on to take some chilly photos, anyway long story short the hanger dropped i hit picked up the rod and felt something kicking on the other end reeled it in and brought up a huge branch that wiped out my left hand rod so after that was taken care of i netted the fish, phoned my mate and told me i would have to do a self take as his car was frozen and wouldnt move as it was -4C, a bit chilly at that.