Hi Oldnut, good on ya for coming into SUP with eyes open and asking questions.
Welcome to the hidden magic that you will discover once you get through the humbling first stage!
A story that may help:
I have also been a committed life long surfer, chasing waves from US to Hawaii, OZ and beyond.
At 55, I had gained a LOT weight due to an injury, when hit sitting at a red light..... but I could surf as well as ever, I just couldn't pop up quickly.
So I decided to get a SUP... just for the
little days when wave size didn't help my pop up.
I bought a Starboard Avanti, 11'2 x 36" wide at 230 liters because I was upwards of 135 kg
I took it out on a river for a test and it was super easy, so I was off to the surf!
Perfect glass at an awesome little reef break, 1 to 2' perfection
Did I mention pure glass?
Ha ha, I fell at least 100 times that day.
My daughter was on the beach, howling with laughter that everyone could hear in the lineup

I managed to get 1 wave on my knees, then stood up.
It felt like I was surfing a barn door

The next day I got 3 waves standing
The third day I was simply surfing again.... on a SUP!
I was surfing that big board well... like I had always been riding it

There is nothing wrong with surfing a big board, except that it was trying to kill me because it was so big it was hard to get away from in a wipeout, because I was quickly surfing well OH
The learning curve is humbling... but quick for a good surfer.
The good news is, there is always a great reason to have a big board in your quiver because SUP opens up so many new avenues in your SUP world that will surprise you as you get deeper into it.
As Colas said: length and width is your friend as you enter into SUP.
Volume is simply float... the real ease of use depends more on shape: fuller nose and hips, with relaxed rocker, maybe hard rails in the tail for easy release and fast speed.
Speed is your friend, like riding a bicycle, balance gets easier as you go faster.
I know how much SUP changed my life, so have spent years consulting with new SUPsters because I enjoy helping people make the transition to SUP
I am happy to help dial in your first board if you want to email me
supthecreek@gmail.com
There is no charge, I simply enjoy doing it!
I dig deeper into you as a surfer, the waves you ride and your goals going forward, to give you some realistic options that match what you are looking for.
And has been mentioned:
The ONE thing you will never outgrow is your paddle
A good paddle can be with you for life
A cheap paddle is a cheap paddle.... good paddles cost money, but it is well spent.
If there is one available to you, ask a good SUP shop to help with your first paddle.