Keith,
You already got great advice from Fishfinder and Beachem. All good stuff
If offshore is your main intent, you may owe it to yourself to look at some of the offshore style of kayaks. By that I mean the Prowler by Ocean Kayak, the eXtreme by Malibu Kayaks, the Tarpon by Wilderness Systems. And if you may like pedaling instead of paddling, the Hobie Kayaks offerings. By the hull being more streamlined in addition to being longer and a bit narrower, they'll be a bit better at cutting through the water and handling chop and swells than some of the shorted/wider ones can. That's not to say the shorter/wider ones can't by any means. They can and they do.
When it comes time to test, some dealers will apply any rentals charges towards your purchase. Also most will let you test a few models after one another so you can see the differences in the hulls. Also be sure to ask if the kayak you're looking at buying is a first or second. Some seconds are cosmetic blems, some have had a hull defect that has been fixed. Scupper areas are big for molding problems, also the tail of the kayak can have problems with flows when being spun. Cosmetic blems are often a decal looks bad, or an area of the surface is not the same as the surrounding area.
Seats are very important. Most supply good back support, but those with a thin butt pad can be trying at times. Sometimes there is not enough padding on the bottom, and the circulation to your legs gets hindered. Some are not bothered by this at all, others it seems to bother more. I use the seat like Beachem pointed out, and have been very happy with it. It has greatly extended my comfort range in the kayak.
The comment about keeping it simple is very wise. Alot of us carry alot of gear and get too involved in buying accessories before we know they will work for our needs, or learn how to really handle the kayak.
Lessons are a smart start. I think basic kayak lessons and a surf zone lesson is always good. Pick one where they teach you how to re-enter
your kayak from the water if possible. Trying it a few times in calm waters would be a good idea in my opinion, you just never know.
Hope this helps a bit, Take care.
Perry