I'll tell you the truth, when I had a weave NOTHING made my hair or scalp feel clean. Even with a sew in, I just couldn't get in there enough to remove all the residue and dandruff. I ended up taking it out in two weeks ($100+ down the drain) because my scalp had turned red and started peeling like something crazy.
I'd definitely recommend LIGHT oils, like coconut or sweet almond. Dilute them if necessary with a corn oil, it abbsorbs quickly and washes out easily. Jojoba, Avocado, and Shea were too heavy for me to easily remove while in a weave. .
Keep your scalp as clean as possible. When the itch got bad (by day 3) I'd swab the parts with a bit of tea tree oil (using a q-tip), eventually it would spread to all of my scalp and keep me "cool" and comfortable. Even with a cap, the oil would still slip through and offer relief.
I'd definitely stay away from greases and waxes that can attract build up; as these may be harder to remove from weaved hair.
Keep your body moist by drinking plenty of water and consuming a flax or fish oil vitamin (or plain fish in general). Keeping your scalp moist from the inside will improve your hair's performance while it's in the protective style and being moisturized externally.
HTH-