If standing is a priority, you have pretty much
upped your price/budget in order to get one
that is super-stable.
Now we all have different points of balance,
centers of gravity, and so on. I'm shorter, so my
center is lower. I have great balance in my
Native Ultimate 12, and can stand and fish in
pretty rough waters (white caps, high winds)
without any fear of tipping.
Your best bet is to find a kayak store near you
and see if they have any yaks you can demo.
OR, you can always add pontoons afterward
that can enhance your ability to stand.
So either of the options already suggested are good.
You can also pound the pavement (so to speak) and
look for a used Native Ultimate 12, a Wilderness
Systems Ride, Wilderness Systems Commander, a
Jackson Cuda, etc.
These are all made for standing and fishing.