re: Android Advice: Need an app to run my home screen, etc. TouchWiz replacement

Nova. I've been happy with it.

You can and maybe should try the free version first for a week or so. If you like it, get the paid/prime version.

Apex used to be considered a strong competitor to Nova. Seems like it's lost a little bit of steam, but if you don't like Nova or TouchWiz, might be worth a try.

If you like to constantly fiddle with your layout and similar details, a lot of people like Buzz Launcher. It's not my bag.

I have considered Everything Me launcher: it supposedly learns how you use your phone throughout the day (maybe in the morning you read news sites, after lunch you play games, evening you do other things with your phone, etc.) and rearranges your phone throughout the day based on how you're most likely to use it. It seems like a good idea. I just expect that my own usage is a bit erratic and I have so many apps on my phone that I think it might annoy me if it guesses wrong and I can't find something easily. But if your use is simple, I can see it being helpful.