I kind of get a little warped out of shape when people talk about getting a "good beginner's" instrument (uke, guitar, what have you) especially when looking at a second instrument.
All too often what people mean by "beginner's uke" is one that's not too expensive - unfortunately, the worst thing for a beginner is a uke that is too cheap. Beginners learn faster with fewer false starts and failures when they begin with good instruments. If you get an inexpensive uke with poor action and poor intonation you will often be discouraged and you will simply never develop a good ear.
Fortunately, in your case you're looking at ukes around $200 and there are some pretty good options at that price range, assuming that you're looking at a soprano. That will get you into a decent uke set up by a pro like HMS, etc. or a Mainland soprano, maybe a Bruko if you're in Europe or can find a good deal on one over here. If you are going to buy a Kala I strongly recommend buying from a real, no-kidding uke dealer who sets them up - even Kala's top end models are very hit and miss on the setup. You might also check to see if Pono still has their sale going on seconds - from everything I've heard they're set up well and the blemishes that make them a second are pretty insignificant.
Whatever you do, don't settle! This is your second uke, get one that is good enough that it could be your last uke if necessary. If that means you need to wait a couple of months to spend a little more, go ahead and wait, it's not like you don't have anything to play right now. Get too little uke and you'll be looking at needing another upgrade in a few months or another year. Get enough uke that you'll never need an upgrade (though that's not to say you might not want one, of course).
John