A common Rock guitar trick is the standard barre chord E shape and A shape. You can literally play anything with those two shapes, if you want to get fancy maybe lift a finger here and there to get a minor or a 7, but it is true.
In the ukulele universe, I have found the same is true with the A shape and the F shape. B is just the A-shape barred and moved up. Lift one finger, get the 7, lift the other, get the minor, leave just the barre, get minor 7th! It's a bit more complicated with the F shape going to minor and 7th, but with those two shapes moving around the neck you can play almost anything. It's also a great way to sound out a song, and then you can go back and use the open chords once you figure out what the roots are.
I never had trouble with B/Bb or D on ukulele, but the E chord is still tough for me to sound clean every time, especially when I have to change quickly. I cannot place three fingers on the top three strings like I do for a D and then add my first finger, so I have to do a partial bar. It's just practice though!