On long routes with a screw belay at each station the number of screws go up. I usually carry 17cm screws for running pro and a 22 or two for belays. I find that the 17cm are a good compromise for running pro as they are faster to place and have decent holding power in good ice. The 22's are also good for nice deep v-thread rappel anchors.
I have used the BD Ice Clipper and a Trango Ice Screw racking device. The BD seems better. I place 3-4 screws on the clipper, 3-4 on a biner on a shoulder sling. The rest on biners on my harness. Runners, draws, screamers and such go on the shoulder sling. This allows access to the gear with both hands. If I were to rack all my screws on one side, on the clipper, left hand placements would suck.
I have used this system for a number of years and it works well. But YMMV.