Last year I've bought my first Android phone after using iOS exclusively since the iPhone 4 came out[^1].
Buying a new phone or switching OS should be the strong motivator you need to just start with a clean slate, but it shouldn't be your only option. You can do it even on your existing phone (always make sure to have a backup so if something important is missing you can still recover it).
The first thing to do is to reset the phone to factory settings and configure it as a new phone. In this case with it being a new phone, you have no alternative, but if you're doing the cleaning on a phone that you are using and you decide to restore from a backup it is way too easy to keep the installed apps without going through them one by one. The approach needs to be different.
Make sure to only download the apps you need right now. For me, those apps are Whatsapp, Firefox, Dropbox and 1Password. Everything else can wait. The first time you need an app download it. It will only take a few minutes more to download it in most cases, but the saving in both lost time, free space, and real estate are huge.
An example of this method in action: I went to Poland last month and I've only downloaded the offline GPS navigator the day before leaving. It got promptly uninstalled once we got back to Italy.
I can finally count the apps I have installed with a two digit number. There is not a magic number you need to hit, it is different for everyone based on where you live, how much tech savvy you are and what are your hobbies. The goal is not to force you to have fewer apps necessarily, but realize which apps you use and make a conscious choice to install them.
[^1]: Actually I've used it on an iPod Touch 1st generation for even longer