What is the maximum sub-panel amperage I can use, and is my setup okay?
That cable's absolutely worthless to you in this situation...
First off, that cable's worthless for what you need it to do, as NEC 338.12 point 2 says that type SER (and SEU for that matter, not to be confused with USE) cables cannot be run underground, conduit or no conduit:

338.12 Uses Not Permitted.


(A) Service-Entrance Cable. Service-entrance cable (SE) shall
not be used under the following conditions or in the following
locations:

...

(2) Underground with or without a raceway

...and you're better off just slapping a fat conduit or two in anyway
Besides, starting with the wire is an absolutely backwards way to do things, especially considering that installing fat conduits (a 1.5&quot; or 2&quot; PVC for power, and an additional 1&quot; PVC for telecom if you wish) in your trench means that you won't have to dig things up later if you decide your shed needs MORE POWAH.  You'll want to use prefabricated sweeps to bring the conduit up at each end, along with expansion joints to take up ground movement.  You'll also get a slight benefit with regards to burial depth here, but it's not enough to be particularly significant, so going down 24&quot; is recommended anyway.
Once you've done that, then you can pull a bundle of individual THWN or XHHW-2 wires through the conduit for your hots, neutral, and ground, getting to pick the gauge of wire based on how many amps your shed plans actually call for and how much load your service can support instead of having to limit them based on the cable you have on hand.
GO BIG OR GO HOME
The other factor is that there really is no limit as to how many breaker spaces you can have on a single feeder, and nobody ever complains about having too many!  As a result, I'd grab the biggest panel you can find, space-wise; in fact, I consider a 100A or 125A, 24-space panel the bare minimum for a generic outbuilding situation.  Note that you'll want a main breaker panel here so that you don't have to provision a separate disconnect for the shed; it doesn't matter that the main breaker in the subpanel is bigger than the feeder as the feeder breaker in the main panel is protecting everything anyway.