A quick and easy check of setup: (Others may want to chime in on my method or recommendation.)
Put a towel on a table. Lay the uke on its back on the towel.
1. Measure the gap between each string and the top of the fret at the 12th fret. It should be about 2.5 to 3mm. Less than 2.5 could cause string buzz.
[Saddle too low, or neck back bow?]
2. For each string, simultaneously press and hold frets #1 and #12.
Then, using a free finger, lightly tap each string at the 5th fret. Look carefully; there should be at least some tiny gap. If there is no gap at all, that may a source of buzzing. [Neck back bow?]
3. For each string, press and hold at fret #3.
Now tap each string at (on) the 1st fret. Again, look for a very tiny gap, as no gap there could also cause string buzz when strumming an open string. [Nut slot cut too deep.]