Been paddling a SUP for the last 4 years.
Yes length and width make a difference but size and weight of user will make a greater one - as does the construction of the board.
10ft 6 is usually 34" wide, is the general purpose size, its fine for messing about on a beach and paddling short distances but will want to go left and right a lot more than a longer narrower board. I know people that paddle 10ft boards and do a 6 sometimes 8km route though they are just slower and more effort than a longer board.
11ft and 11ft3in in either 30 or 32" is the "sport" size, tracks in a straighter line more easily, better if planning on more distance paddling, and dont want the full touring board (12ft6 and longer)
If you are too heavy for the board you will find it bends in the middle too much and its less stable and will also sit lower in the water and you will be standing in a puddle. The correct board will let you paddle without water sloshing around your feet
Dont buy dirt cheap boards, there is no British Standard so you can sell a binliner as a SUP if you can seal it and blow it up. A lot of the sub £300 boards are not designed to take an adult male despite advertising as such, and while you might hear of some fantastic customer service - they take your money and dispatch straight away! or they replace faulty boards without quibble - just every other customer has a faulty board! There are a few brands that have a better reputation - Red Paddle/Naish/Starboard/SIC are the top level, Gladiator/Fanatic middle ground. I have not heard bad things of Fatstick/Sandbanks that are at the lower end but dont know anyone that paddles them.
Im guessing you dont plan on starting till the weather warms up?
I take it you are in Cambridge given your signature, I would find somewhere that rents out boards or try before you buy and try both sizes. A quick google search shows several,