I'm mostly playing for fun, but I want to get better at the same time in a systematic way.
Figure a lot of you are similar to me so just want to pick your brains :)
For number one, figure out chords and scales. These are key shortcuts to harmony and melody, to soulful accompaniment and wicked solos. Practice different strumming patterns to achieve different rhythms.
For the second, look up uke tabs to songs you think are fun. Find someone who wants to sing or can back you up on trombone and work on learning songs together. When you can play songs, alone or with others, start adding your own twists to them - slow down during the third chorus (tempo), crescendo in the B section (dynamics), try using your uke for percussion in between strums (timbre). Remember whenever you play, that each performance is an act of creation in and of itself.
Lastly, record yourself, and listen, and work on the things you thought sucked.
https://www.dummies.com/art-center/music/ukulele/ukulele-for...
youtube is good resource too
good luck