I'm in a WS Commander 140. It has a bench seat that makes getting up and down fairly easy. The Commander is crazy stable, but not self-bailing so not a good choice as a big water kayak. I haven't yet taken a tumble out of the kayak that I got in 2012. I didn't stand a ton at first when I got the kayak. It took a little while to get completely comfortable standing. Now, it's second nature. The Commander might not be made anymore, but there seem to be a lot of recent models aimed at being stand up worthy.

I have a Commander 140 and it depends on the type of fishing I'm doing if I'm standing or not. If I'm in the shallows I'm standing most of the time. If I'm fishing out deep there isn't much advantage there for I sit. It's also nice to stand to let my old body stretch out from time to time. The Commander has to be one of the most stable kayak I've been in.

Check out the Pelican Catch 120 if you are looking for a cheaper model standup style kayak, I have one and ise it more than our Jackson cruise 12. The kayak is super stable and paddles quite well for a big barge looking kayak

I have a Native FX Ultimate and a FX Propel and both are very stable.
Also there are a few guys fishing from the Diablo's and they claim to be one of the most stable yaks for standing.

I have the same kayak and for the money its great! Great comfy seat, not super heavy, I found that it paddles easy even when standing and at $750 I can't find another kayak with the same features cheaper. The only other model that comes in close is the vibe seaghost 110 but I'm not sure if it is as stable as the catch 120. It is a barge but for me it works for my style of fishing.

I've tried outa Diablo and it is beyond a doubt one of the most stable kayaks I have been on. I'm not fond of the seat though. And I actually felt it was tougher to paddle while standing than my Pelican. If I could find a killer deal on one I'd get it though. I have a buddy who has a Native slayer propel 10 and it was super stable for me too. Nucanoe makes some awesome stable kayaks as well!

Never have stood and never will. That's just a physical limitation of mine. Still enjoy kayak fishing.

The Enforcer 120X I have is definitely not good for standing, however I always out-paddle everyone else in their super-wide kayaks and leave them behind!

I've never tried to stand in mine. When I watched a promo video, the guy in the yak stood up, made a few casts, and sat back down. But, he must have had tons of practice or perfect balance, or both. There's no way I would try it unless the width was at least 36". Mine's 28". As far as speed, I bought one with a built in troll motor, because where I fished, I would have worn myself out before I even got started if I would have had to paddle to the fishing spots. If you want to be able to stand, buy a wide bottom. You won't regret it. Just my opinion, and you know what's said about opinions.

I have the Ascent 128T.... Worth the money! you cant flip it if you tried! I stand in it constantly its amazing.

I mostly fish out of my SoloSkiff, but I also use an OK Trident 13 and an OK Torque. Both are easy to stand in, but I have fallen out a couple of times while sitting down. It seems that the colder the water and air temperatures, the more likely I am to fall out. They generally feel "shakier" than they really are.

Something else you might consider is a stand assist strap?
STAND ASSIST STRAP