I think you have two questions to answer:
1) Do you want a shoertboard or a fish style board. Fish and shortboard two different animals.
2) How small do you want to go.
I like the fish style boards. I like a skatey feel. I have friends that don't. Personal preference.
I ride boards of all different sizes, but being heavy with shorter legs I always wanted a board that would let me pretty much plant my feet and go, without much worry about moving fwd, backward.
On a traditional shortboard, if I want my feet in the ideal position to generate speed, my rear foot is too far forward to be in the ideal position to lay down a hard turn. I have to move around. On my fish style boards, I can pump and lay down hard turns without moving my feet around. It's a nice change of pace. And as I said, I like a skatey feel, not for everyone.
For reference, I'm about 6', inseam only 30", arm length 37", weight between 210-20lbs, so yes I really am built like an ape. My shortboard (fish inspired) is 6'5". My fish style board is 5'11", and carries 15% more volume than the shortboard. Both custom made by a shaper for me taking my size/input into consideration.
I also ride bigger boards up and over 9', but not as frequently. One of my favorites of all time is approxametely 8' long, shaped in a fish style, and it's so wide even I have trouble carrying it under my arm, so I'm not afraid of foam at all, but I prefer the responsiveness of a properly sized shortboard or fish.
Since you dimensions are what would be considered average in the surfboard shaping world, off the rack would fit you easy 9doesn't fit me well). If I were you, I would test the waters with used boards to find out what you like out of a smaller sized board before buying new. Definitely try to ride a fish first before committing to that style...not for everyone.
I have no idea what Dame Reynolds, or any other pro rides these days...I'm old, and ride what i like, but I still like shorter chunkier boards. When the potato chip craze was in vogue, I was riding old school fatty 80's shortboards, then a flyer, then tried out a rocket fish, spent some time on a CI Flyer, then moved to a true fish, then variations on a fish that suit me (round tails, weird for a fish I know).
I always gravitated to a less than typical shortboard, regardless of what Dame or anyone else is into (yes I'm old). My long winded point is, just try stuff and decide what you like. It's fun surfing all kinds of boards. For a while I searched classifieds and garage sales and bought all kinds of weird boards. Was awesome back when I had the time to experiment and try different designs. I found no matter how many cool looking old single fin boards I bought, I didn't mesh with them, but then I would love a weird fat hot pink thruster from the 80's, go figure.
off my soapbox now :-)
One last thing, your dad is probably just trying to prevent you from going to lean. There's nothing worse than riding a board that makes it really difficult to catch waves. You can't fault him for that. Err on the side of too much foam rather than too little while you're figuring things out, but if you can eventually get the size dialed just right, it will propel your surfing abilities.