WARNING: wall of text ahead, but detailed answer therein :music:
If you are not going to move around on stage at all and can pin your feet such that your instrument stays in place in front of where the mic is set from your pre-show soundcheck, then you do not need a pickup.
OTOH, of you want freedom of movement, or intend to prance around the stage like Taimane Gardner, a pickup will be required.
Having said the above, due to the immutable laws of physics, both the most elaborate expensive pickup, and/or 'best' mic will
not ever render the sound that you yourself as a player hear with your ears.
This is a fact of science based upon our human hearing and the limitations of audio transducers, in that none of them respond the same way as the diaphragm of your ear drum.
Striving for this is a slippery slope and fools errand, and many companies have made a valiant effort to 'approximate' the natural acoustic 'in-air' sound of the instrument, but just HOW accurate or authentic the sound is rendered, is so completely subjective to the
listener that generalized, blanket statements are usually anecdotal manifestations of bias confirmation, cooked up to rationalize against buyer's remorse, especially if the mic or pickup is 'expensive' for the buyer.
LR Baggs Five.0, Mi-Si and K&K are all affordable to most of us. Sure more exotic options exist, but crossing the point of lesser returns is easy even if only spending a little bit more.
$500 for a pickup???? nahh, 30+ yrs of audio engineering experience tells me this is previous tech wrapped in some new shiny box and pretty much just snake oil.
There are many OTHER variables in the signal chain between your pickup or mic output and the end speakers in the amp or PA that will be the output where the audience will hear your sound, and all of these can make a great pickup or great mic sound like crap, and usually make a crappy pickup/mic unlistenable.
Some may want to defy reason and try to get a silk purse out of a sow's ear and go 'cheap as chips' all the way, but doing so will only punish the audience, while depleting your funds that can be used to get better equipment.
'Buy cheap, buy twice'.
I have pickups in about 1/3 of my ukes, which are more than 2 dozen as of now, but I am not playing out live currently, and mostly just recording at home and for that, I have a spectrum of different kinds of microphones that I use.
If I was to do an open-mic thing, I'd rather actually use whatever mic is there on the stage and not even worry about it. I do not hop around when I play so being in the mic's sweet spot is not an issue for me. Open mic is about
gaining performance experience and not being OCD about the uke sounding exactly like it does when I practice at home.
If I was in a band situation and had more control over the sound shaping, then maybe I would use a pickup and some pedals, but there would be lots more planning involved for this that would make all of this worth it.
Installing the LR Baggs, Mi-Si pickups is NOT rocket science and each only requires the drilling of 3 specific holes, and K&K pickup requires the drilling of only 1 hole, and each of these has a hole for the endpin jack as one of the holes.
Anyone with a drill and lots of finesse, patience and attention to detail can install one of these pickups in less than 30 minutes. Lots of tutorial videos exist on YT.
So pickup now vs. no pickup vs. pickup later?
It should NOT direct which uke you buy, for any uke with an included pickup, whereby the electro uke sells for less than $300 USD is NOT going to have an LR Baggs, Mi-Si or K&K pickup but some cheapo (Belcat or other Chinese) pickup that is using noisy electronics based upon preamp circuits from 20 yrs old tech that is not desirable for audiophile sound because they have lots of self-noise that manifests as 'hiss'.
So, you can get a better uke WITHOUT a pickup for your budget price, and then later have ANY pickup installed or do it yourself, spending ~$150 USD for the pickup itself from a reputable vendor.
Doing the pickup AFTER, with a quality unit, both YOUR ears and your audience will thank you for it.
/stepping down from soap-box/