think I'd still look for a 12' or 13' boat, and you want a sit-low option for wind - tall, adjustable-height chairs are showing up on most new boats these days.
Longer boats are more buoyant, as in they float shallower for the same load, and also track better.
If standing is not in your plan, the more narrow the better - the other way if you want to stand, wider is better.
Keep in mind paddling 2 miles is more work than you might have guessed, especially when you add coast wind.
A used Heritage 12' Angler or Redfish might be just the starter boat you're looking for, especially cost-wise. These boats sit low, track well, and spin well to turn. Some people also stand in them, but I would look for a wider boat for that.
If you want a new boat, best plan is find out when ACK has spring demo days, also if you can travel to San Marcos, TG will demo boats for you on the San Marcos river just about any day. Texas Kayaks in Boerne demos on Boerne City Lake with an appointment - maybe you can find a local kayak shop that can demo boats and go try some.
As far as essential equipment, stake-out pole and/or anchor, and I find a drift sock and trolley invaluable for flats fishing. Paddle leash, first-aid kit, tools, lines, duck tape, sharp-sound device (whistle works). Useful are rod holders, fishing crates, a cooler/lunch-box, dry storage.
You already know pfd, but your pfd should have a high back that clears a kayak seat back-rest.
Also don't buy a cheap paddle. Werner fan here, and the $250 Werner paddles are excellent - good internet shopping can find size and color overstocks for $200. Though since a spare paddle is a good idea anyway, can cheap out on a first paddle and upgrade later - just keep in mind, weight and especially flex in a cheap paddle is energy that could have you home by now.
I'll throw up my rigged Tarpon photo - this is a 16' wind-and-distance flats boat. 28" wide, sits low.