Chamberlain (and Craftsman et al rebrands) are everywhere so it is easiest to get parts for them, cheaper through 3rd parties.
There's probably some site that has pros and cons for each drive type. I formerly had a chain drive and it worked fine but I disliked lubing it so switched to belt. The belt wore out in a bit over a dozen years of use so had to buy a new belt, though the only place it wore much was right where it rested on the pulley at the door end.
Chain needs adjusted when you install and "maybe" adjusted later. Belt needs adjusted when put on and definitely later but this is just turning a nut a few turns, if you never do it, it may not matter unless it is sagging down on a greasy rail while you don't want a belt to get any grease on it.
Screw drive, I don't see the justification to spend the extra money.