Yes on the check valve, for the reason you guessed. How fast does your sump fill? I'd go with the lowest hp that will keep up with the fill rate.

Time the sump fill, measure the sump l x w x h x 7.5gal/cuft, divide by minutes to fill = gal per min pump rating needed, select next pump size up. Pump gpm is given at a stated feet of head, or the combination of feet of lift plus friction loss in the pipe and fittings stated in feet of head. Unless you have a very convoluted pipe run, figure 2x water lift for the total head required as a rough rule of thumb. If you are close, or worried, let me know and I can calculate the piping head loss from a dimensioned and sized diagram of the piping.

I would buy the std old mech switch type pump. Float height is usually adjustable with sliding rubber washers on the float rod at the pump switch.