south Texas has some great open ocean kayaking oppertunities. i know a kayak builder down around Galveston. haven't talked to him in years.........
anyway........
check out your local buy-and-sell/classifieds/craigslist. look for a kayak 16 to 18 feet long, 20 to 24 inches wide. your price range suggests a plastic rotomolded boat. i had one for two years and just recently bought another one. they're almost indestructable, but store it out of the sun, or UV will fade the color.
about performance:
a longer waterline will be faster.
a narrower beam will be faster.
both of these combine to make a boat that is easier to propel to hull speed; therefore, more efficient. but all things are trade-offs. a long narrow kayak with a round hull shape will be a bear to keep upright.

it'll be fast, but tippy. i like it that way, but many don't, prefering boats that have some inherent stabilty.
about comfort:
a kayak is not a canoe. it is a watercraft that was invented thousands of years ago by peoples that needed an efficient method of travel on water for the purpose of hunting for their survival. Aluets and Greenlanders predominantly, but peoples all over the Arctic built variations on the theme. production kayaks of today are mostly based on the Greenland style of boat. sort of. we have seats to sit in, and braces to put our feet on, and backbands to hold our lower back, and thigh hooks to lock us in the cockpit. all these things are adjustable. in essense, we
wear our kayaks. it's a nice feeling to have a properly fitting kayak perform for you with the slightest shift of weight.
when you first start out, even a 24" wide barge of a kayak is going to feel tippy. it won't for long. you'll very quickly learn how to use your new "feet". do you remember how it felt to learn to ride a bike? (i do. my Pa holding the back of the seat of that old green coaster-brake bike, running along beside me.

) learning to kayak is easier.
check around your area, and see if you can rent a kayak. it might be tough if you are too far inland. hey! i just had an idea!! move to the PNW where it never gets over 90* and it almost never snows ('cept for last winter

)
if you have more questions, i'm happy to answer them. in spite of what RG says, i'll be around till sunday afternoon.
Daren........