Finger placement when fingerpicking a melody

Hello, I’ve been working on learning how to fingerpick, and I’ve run into a problem. Fingerpicking patterns and arpeggios are going fine and make sense to me. The problem is when I try to fingerpick a melody it all seems like a confusing mess. I think my questions are basically these:

First, with the left hand, how do you decide which finger to use to fret a particular string? Tabs don’t indicate which finger to use, so I’m left guessing, and it just feels so random. I know ultimately you can do whatever you want, but there must be some kind of rule of thumb or logic to how you decide. Like if you sit down to learn a new melody you’ve never played before, how do you figure out which fingers to use to fret which strings?

Second, with the right hand, when I fingerpick a pattern, I usually use my thumb to pick the G string, index to pick the C string, middle to pick the E string, and ring to pick the A string. My question is what to do when I need to pick the same string multiple times in a row? Is it best to just keep using the same finger multiple times, or better to alternate between multiple fingers? Again, I know that ultimately you can do whatever you want, but what’s the general advice on this?

For the left hand:
If you are playing arpeggio patterns, one would naturally hold the chord shape the usual way, there should be suggestions online as to how to place them.
When playing a melody line all is fair game.
However, if you are playing chords in between or are thinking about doing so, I would try to form the chord of the song in an inversion that includes most of the notes needed. Then add or subtract fingers if you need notes that are not part of the chord.
You would need to find out which of the several ways to play the chord is appropriate. And if the melody uses a lot of notes which are not part of the chord, the benefit is not big. But thinking in full chords can help remembering what to play.

For the right hand:
It sounds like a good approach that you have.
I usually just uses the same finger multiple times on the same string if needed, unless something makes me feel like doinf something else. But I am not a maestro.

Right hand technique: To be honest, the only really important thing to keep in mind for your right hand technique is that it should always be relaxed. If double picking a string with your index finger makes you tense up, consider picking it once with your index and once with your middle. Take it on a song-by-song basis, and find what works for you- the best option will be the one which allows you to play the melody while remaining relaxed and in control.

In classical guitar, it's common to shift the right hand up and down the strings in order to play the melody. This, I believe, can still apply to uke. I would recommend looking up classical guitar fingerstyle technique and learning about your options.

For the left hand, try to keep fingers 1,2,3,4 (index to pinky) aligned with the frets 1-4. Move the left hand up or down the neck as needed keeping the relative position of the fingers. Exceptions to this rule are common, you're looking for an economy of movement and good fretting. No need to put down all the fingers of a chord when you're finger picking.

for the right hand, alternate fingers. Using the same finger multiple times is inefficient and not as fast as if you alternate the fingers. Let the fingers walk on the strings. Don't use the right pinky, and don't let it rest on the soundboard, keep the hand loose and free.

Keep practicing and good luck

Eugenio

For the left hand the suggestion with chord shapes was right on. Further you can also assign a finger to each fret ie. index on first fret middle on second and so on and then practice runs in this base position. It is easier to keep the fingers stable in their home and move them up and down the strings than jumping from fret to fret.

For right hand watch some videos of pros who play solos. Many soloists use just their thumbs for all picking and anchor the hand with the other fingers for stability.