Uke players are pretty laid back about how or what you want to play. I started w/wanting to use a pick & bought a few really thin Dunlops & some rubber "Wedgie" picks. Then after awhile I got used to using my index finger for most strumming & dropped the picks. Do what works for you & doesn't keep you from enjoying the uke!
You may come across a few uke players who look down on you for using a pick. If you ever come across anyone like that, tell them to mind their own business.
The real issues are that a pick will make it sound different and it will restrict your playing. If you want to sound like the majority of players and aspire to be a James Hill or a Jake, you need to use your fingers. Fingers are much more versatile than a pick and you have four of them to use. I use the thumb and the first three.
Recently, I had to use a pick in order to be able to play with others (broken finger nails). I often play guitar with a pick and I didn't find it difficult, but it did restrict my playing a lot.
As has been said, it depends on what sound you want.
One number that I do is my own spoof version of 'Put the Light on' and this sounds best with a hard, heavy metal timbre, especially plugged into the overdrive slot, so I use a very thin plastic guitar pick.
Something like 'Putting on the agony' benefits from some alternated thumb & fan-strokes so I don't use a pick for that one.
I've always played uke with fingers, but hate long nails so I get a really soft mellow tone... so I've just bought a set of Fred Kelly finger picks instead, my ukes are now much louder and clearer in tone, though I have found restrictions with them such as no finger tapping. Don't just expect to be able to use them, its like learning a new technique and will take a bit of time and patience.
All the above comments are bang on - it is up to you.
Fingers are more versatile, and certainly more traditional, but it's your uke
All I would say is, if using a pick, go easy with it - ukes dont have pick guards, and those nylon strings wont stand up to metal strumming in the same why as steel strings will.
Currently I'm using a fred kelly slick pick (thumb pick) and bare fingers. Although on some songs it's just the bare thumb and fingers. I've only been playing 6 months so i'm still finding my way around the uke.
Oh I almost forgot, there is one song that I use a flat pick (plectrum) on.