I have been surfing on a mini mal 7.4 – 21 ½ - 2 ½ for about 30 times and know how to turn a surfboard on the face of the wave.
I am 145lbs (66kg) and I am considering of buying a fish (not a retro fish).
My question is should I buy a 6'3''-20 1/2 - 2 3/4 or a 6'6" - 20 3/4 - 2 3/4 ?
As a first shortboard I would recommend a thruster. I have tried my friends quad and it felt quite different underfoot.
Since your minimal is probably a thruster, I would change one thing at a time and go with a thruster shortboard. Once you can control that then you can fiddle around with fin systems. If the fish is three finned (rocket fish I think they are called) then that should be fine, good even.
The dimms you posted are very thick too (2 3/4"), I (at 152 lb) could probably just duckdive 6'6 (but not very deep); the 6'3 might be duck-divable for you but it will be hard. If you are ready to move to a shortboard, then something with the same dimensions as above but a bit thinner would be preferable. I personally use a shortboard to duckdive so I can get out on bigger days (my local is one of the hardest paddles in the UK), so I don't see the point in one that I can't duck-dive; if that is different for you then I would ignore this paragraph.
I think it would be good to stay on a minimal until you really have that dialled.