"Future capacity" is job one when installing a panel. Think big. Make sure you never run out of spaces. Small "main breaker" panels tend to have very few spaces, so I recommend aiming for spaces and disregarding main breaker or panel capacity. It doesn't matter anyway; read on.
6/3 NM-B is the legal minimum cable for that run. You are a long way from worrying about voltage drop for distance reasons (I don't even bother checking til 110'). You don't need to worry about "wet locations" so NM-B will suffice.
Cables in a ceiling space are usually not a problem, but there is some technical stuff about plenums (air handling spaces) that I'm not up to speed on because I just avoid them.
The subpanel does not need any disconnect switch since it's inside the same building. You might as well use a main-lug panel. Just FYI, if you did need a disconnect, and you used a main breaker, size doesn't matter. What matters is the feed breaker. There's no practical way to coordinate trips so the nearer breaker trips first, if that's what you're thinking. A 30A feed supplying a 225A sub is fine.
Copper #6 or aluminum #4 is officially rated for 55 amps. 50A is fine. However *you are allowed to "round up" to the next breaker size, so 60A is a free upgrade!
Going up, #4 copper is good for 70A only. #2 aluminum is good for 80A (75, round up) and #1 aluminum is good for 100A. (at 100A, you get a free "bump" because you're now allowed to use the 75C thermal column in the big temperature/ampacity chart. Aluminum is much cheaper and perfectly safe for large feeders like this; just use the goop and torque to spec.
Look at your excellent diagram. Note how you have the two subpanel breakers abreast. In normal panels, both of these are clipping onto the same panel bus bars, which for some reason are called "stabs". Now you have to start worrying about stab limits which are stated in your panel instructions. I recommend dodging this issue, by staggering these so your subpanel feeds are sharing their stabs with ordinary 15/20A branch circuit breakers.