In general, anything that is useless when wet, is very inconvenient when wet, is uncomfortable when wet or is destroyed when wet should be in a dry bag or dry box. There are several types of dry bags:
Dry bags are made of several weights and types of material. For sea kayaking, only relatively light fabric ones are required. The heavier ones that are used in canoeing are overkill. Vinyl (clear) dry bags seem like a good idea until you realize how difficult it is to deal with the sticky surface when trying to load your kayak.
Getting air out of a dry bag.
It is possible to get the air out of a dry bag. Put your stuff into the dry bag. Fold the flap over (if it has one). Without closing, fold the closure part of the bag over the stuffed part of the bag and push down - this will squish everything and expel the air. Quickly snap the closure up and fold it over in one motion. If you do this right, the bag will look like it's been vacuum sealed.
You can make your own dry bags using heat-sealable fabric. Instructions are available in Sea Kayaker magazine - Issue 88, June 2002. See: How to built your own.