Hi Switchfoot, welcome!
An intermediate board probably just means that it's more flexible and forgiving. Beginner boards usually mean that they're cheaper and lack features (since manufacturers may think that beginners often aren't snowboarding in ways that take advantage of the features). So really, any 'beginner' or 'intermediate'... or even 'advanced' board is fine for you, though you probably should be wary of the word 'expert'. Really though these are just simplifications so don't get stuck on these terms.
It depends on the snowboard, but I think 149-152cm roughly should be fine for you. Other people can probably narrow down specs better.
There are *so* many snowboards out there, that it's hard to really make recommendations.
Some things you can think about: there are 3 major snowboard profiles/shapes. Camber (harder to learn, but forces you into better habits which makes it easier later), Reverse Camber/Rocker (easier to learn, but easy to develop bad habits), and Hybrids (sort of a middle ground between the two, but these are more expensive).
Another thing you want to think about is do you want a True-Twin snowboard (useful if you do a lot of switch riding), or a Directional snowboard (which might be slightly better in powder, or at higher speeds).
That will help you narrow down your choices.
Then you pick bindings to match the board: this is primarily based having compatible flexibility/stiffness, but generally speaking you're probably going to aim for all-mountain bindings. Mostly you just pick by durability, reputation for reliability, and looks.
If you want to start looking at snowboards, some well regarded brands are Never Summer, GNU, Lib Tech, Arbor, Signal, K2, Ride... and of course Burton (which makes good snowboards, but they tend to be pricier... they're kind of the 'Nike' of the snowboarding world).