Depends on how accessory crazed you are. Some gotta have every do-dad, the more expensive the better. I've been kayakfishing since the first Ocean Kayak came out around 1970. One rod and reel and a bag of scampis was it for me. The simpler the better, eskimo style. My mottos, never be any farther out than you can swim back, and Murphys Law: the more crap on you yak the more likely you'll flip in the surf. But since than, the manufacture of extras has gone nuts. Start simple and see what you can't live without.
Essentials: rod and reel (I like the cheap stuff, $30 UglyStiks don't break your heart when you lose them/ E Bay reels like Penn Squidmaster $30) Some guys have 5 or more rigged up with different stuff so you don't have to retie different lures. plastic box with assorted lures, hooks and weights, I have a ton of gear but only load the stuff I'll be fishing with. A rod holder or two is nice. A gaff (mines a recurved and sharpened paint roller handle, big fish I use a ball peen hammer to calm them down
) A fish stringer, like for trout is easy to carry, but a lot of guys use a steel fish clip
A PFD vest is probably a good idea, I only wear mine when it's nasty or big surf, but some wear theirs religiously. A pump is good if you have a leak, or at least something to scoop out water in your yak. I found a $3 whistle, temp, mirror, magnifier(To start a fire) that I carry on my vest. Some guys have extensive first aid kit, flares, Radio, GPS, swim fins, tow rope,anchor, drift chute, waterproof paddling outfit, bait tank, the list goes on. I got an Eagle portable fish finder off of e bay for $25. works great, but I don't really need it. All the extras in the world won't make up for experience, so your best investment is your time. Get out there and remember...it's a wet sport. Have fun.
-Scott