10' basic kayak
Skim some of the blog posts on You Tube in the 'White Spot Pirates - Untie the Lines' series. Impressive young solo woman who has run that blog for about 3 years - she gets great use out of a basic 1-person 10' kayak (~$450 new currently; Precision Prodigy): e.g., exploration along interesting shorelines, small grocery shopping trips, visiting other anchored boats, to/from shore for clearing in/out, and even occasionally (and carefully) with a second person on board. Her inflatable tender is usually stowed rolled up below decks until she needs to ferry several people or heavy equipment (300' of new chain, etc).
I'm researching a kayak too, to supplement an 8' hard dink on foredeck as main tender.
My research so far:
First, I decided not to consider a sit-on-top. I didn't want stuff I'm carrying to fall overboard (camera, phone, etc). The following is only about sit-inside kayaks that are from the main manufacturers.
Most of the shorter kayaks (read: easier to stow on the foredeck or side-deck, and easier for one person to lift and maneuver) are for white-water paddling. Don't get one of those: they're designed to give high lateral mobility and therefore they don't 'track' at all, which will wear you out on a long straight-line trip to/from shore - especially in any cross-wind or with any chop.
The shorter 'recreational' kayaks (polypropylene rotomolded mostly) are ideal (compared to the touring or ocean style ones). They mostly have a shallow v-hull hull for better tracking, and 1 or 2 chines for lateral stability, and a good amount of freeboard (so you don't need a skirt). In the 10-11' range, rotomolded kayaks will weigh about 42-48lb. Fiberglass ones (like Hurricane Santee) will weight about 38-40lb.
Some of the more more up-scale recreational kayaks have a small retractable keg (e.g., Wilderness Aspire 100 and 105), but others have a moulded non-retractable 'skeg' that helps with tracking just as well (e.g., Wilderness Pungo 100, Precision Prodigy, Old Town Derigo, etc). You might be tempted to save weight and get a Hurricane brand kayak (nice!) - more efficient through the water, but much less load carrying volume and weight capacity, and more fragile on rocky shorelines.
You can buy cheap after-market plastic skid plates to screw into the fixed skeg to save the hull from wear by dragging the boat on shore.
You'll want to go up a bit above the really basic ones (i.e., <~$350) in order to get a well-sealed aft dry storage cavity for your camera, phone, dry clothes, paper documents and groceries, etc)
If you think you'll be in the saddle for an hour or two at times, consider going a little up-market to get one with a comfortable multi-adjustable seat. Some you can tip way back for napping ;-)
Finally, think about your personal dimensions (LOA, beam and gross tonnage) - different brands have cockpits that are wide or narrow, long or short, and they have wide or narrow overall beam (tipping stability) and different overall carrying capacity (you, and your groceries, etc).
It's been fun doing the research on-line, and I visited two local stores recently to see options in person too. I didn't ask about being allowed to test-drive as I'm not quite ready to shell out $500-700 for the ideal one for my needs.