I've read the threads on how to select a kayak and they are very helpful. I'd like to describe my needs and then get some suggestions for specific kayaks to look at, and try out:

I'm in good shape, but I'm in my 70s.
I fish with a buddy in his boat, but when he is out of town and I fish by myself, I'd like to be able to get in the water and move around a bit.
I don't have room to store a small jon boat.
I can see myself fishing in a large lake, but in a limited section of it, along the bank not far from shore, i.e. I won't need to make long runs.
In winter, I'll fish from the bank, i.e. not in a kayak.
I want a sit-on-top kayak.
I want a very, very stable kayak, speed is not important.
Will want a comfortable seat and back.
Will want as light weight as possible, definitely under 50 lbs, and closer to 40.
Will paddle, not peddle.
I read that at least a 12' length is recommended for fishing, but if it is stable, shorter will be fine with me.
As you can see, if I get a kayak, it will have limited and irregular use, but will come in handy when needed, so I'm not looking for perfection or extreme durability.
Prefer a new price to not exceed five or six hundred dollars.

With that in mind, can you recommend a kayak for me to check out? Considering storage and how to transport it back and forth from the house to the lake (top of my little SUV, don't have a pick-up), probably the only other option for me, other than a kayak, is a belly boat. I have fished from a belly boat, but never from a kayak. Any suggestions or comments will be appreciated. I'm definitely open to suggestions if I'm on the wrong track.

Gonna be hard to find one that weighs only 40 or 50 lbs.

I like santa cruz raptors. The empty weight is 68 lbs and the weight cap is 360 lbs. It isnt slow but as stable as any other yak out there. Made in the USA. Worth a look for sure. I fish lakes mostly but go offshore when possible.

Thanks guys for the comments/replies. Christian Myrick, 68 lbs. sounds awfully heavy for my use, but I'll read up on the santa cruz raptors. Thanks again.

There are lighter yaks for sure...but lighter "stable" ones, its gonna be tough to find. I sure do hope you find the boat for you.

Cobra navigator 12'6", 50 lbs with 450 lbs capacity. I had one and it was a great kayak. Comes with a high back seat.
Ocean Kayak Scrambler XT 11'6.5, 47 lbs with 300 lbs capacity. People I know have this one and it performs well. Also comes with a high back seat.

A little over your price range but should be very stable if they are anything like the other ocean kayaks. Definitely worth a look. https://www.austinkayak.com/outlet/products/1612/Ocean-Kayak-Prowler-13-Angler-Kayak-Blemished.html?utm_source=google&utm_medium=cpc&utm_campaign=Shopping:%20ACK%20PLA&scid=scplp2494153&gclid=CjwKEAjw1KGqBRC55bru-sa7zCcSJAAxsBf5mJpHPiBHiXr-DYWmFvj5mI6NBMwF-xBtYDOLjQDrXBoCDsvw_wcB/

I didn't get the link to work on my above post. Try this one.

Ocean kayak prowler 13

Malibu Mini X is about all that I can think of that comes close to your requirements.

http://www.basspro.com/Malibu-Kayaks-MiniX-Kayak/product/11091707293638/

Lightweight and at 33 inches wide, reported to be stable enough for "some" to stand in.

How about the Native ultimate ? I didn't look up specs but I remember Pelican's being light most people can can stand in them, have the good seat, supposed to paddle nicely just a thought

I hadn't thought about the Ultimate. Would be a great choice!

The Ultimate FX12 would be my suggestion. It is not a SOT and it is more than your budget.

I am 60 and I load mine on top of my truck camper by myself. I have fished just about every lake in the DFW area from mine with no problems. It is extremely stable and the seat is very comfortable.

Check it out: http://nativewatercraft.com/boat.cfm?id=53

If you want to test drive one send me a PM and we'll make it happen.

Ultimate FX 12

I was going to say the same thing: The Native Watercraft Ultimate 12 FX is going to be the closest kayak that suits your requirements (albeit the price). The Malibu Mini-X is another good option, and even though it's only 9 feet long it does a decent job at tracking. The Ocean Kayak Caper is another good option, light weight, stable, and could be found in your price range used. The Cobra Navigator is another option, but Cobra pulled out of the US market about 2 years ago so finding new is going to be a problem.

Unfortunately you're looking for a kayak in segment that doesn't really exist; inexpensive, lightweight, and very stable.

Though possibly not the best fit for you (depending on your fishing style) - I have an Ocean Kayak Frenzy that works well for me and meets most of your requirements above (or at least has for me). I've decked it out a bit which does add to the weight when you launch but not for transport. Its a fun little kayak.
It is a bit shorter than most people would recommend for a fishing kayak - but that hasn't stopped it from performing for me.

Stability wise - i've never turtled in it in the last 3 years. Everyone that has tipped out of it has done so due to overcompensating (due to the hull shape it has two stability points and people over-react when they feel themselves move past the first). In all cases the kayak has stayed upright and the person has tipped themselves off of it. Though i have stood up in it... standing is more an exercise in how gracefully you'll jump out than actually standing

I added on some track for ram mounts, built a little kayak crate, and recently even added a fish finder. All of that adds to the weight but it still clocks about 55lbs fully loaded. I use a flotation cushion under the seat for added comfort - but the seat by itself is not bad at all (just that the extra padding is nice when you stay seated for 5hrs+).