After you get your first ukulele (whether you borrowed, rented, or bought), the next thing you need to do is to learn how to strum. This is the rhythm section.
However, it’s nearly impossible to write about strumming without showing it, so you’ll have to come to one of my ukulele workshops, especially the one called “Different Strokes for Different Folks.” For now, I am going to answer your question about what to do with the other hand: which chords should you learn first.
As you can see from the above chart from Ukulelehunt, the most commonly used chords are C, G and F. I’d say G7 is easier to finger than G. The trick is to hold your hand at an angle, as shown in the video below from my ukulele jam master on Maui.
One thing to remember: to use your index finger on the first fret, middle finger on the second fret, and ring finger on the third fret — by default, that is. To play C, for instance, use your ring finger to press the third fret A-string. To play the F chord, use your index and middle fingers. When you get to the G chord, you’ll need to use the index and middle fingers on the second fret (C and A strings respectively) and ring finger on the third fret E-string.
I discovered a world of two-chord songs, in compiling the next workshop and jam session for my group. Most of these songs use C and G or C and G7. In another key, it would be F and C or F and C7.
So you see, learning C (or C7), G (or G7), and F will get you very far. Try to make a nice sounding tone. Press hard and well. Let the strings sing.
Next, you’ll need to learn to switch between chords. How would you do that?