Go with Ryzen, if you're only gaming. Get a Ryzen 5 3600 and a B450 and get a better GPU with the remaining money. If you're doing work that profits from more cores, get Ryzen 7 3700X instead
I would not get a Intel CPU if you aren't on the plattform already at the moment. I would recommend a Ryzen 7 3700X or if you want to have more compute perfomance a Ryzen 9 3900X. AM4 has a brighter future than 1151v2 since it seems that the new Desktop CPUs from Intel are gonna need new...
The RX 570 4gb is a killer deal at the moment. I'd really recommend that card.
I'd think of trying to get a used Ryzen 5 or something but the 1200 is ok.
I have the same notebook. The only difference is that I have more storage.
I experienced some not very strong throttling but not really bottlenecks like you seem to experience. And the throttling goes away if I plug it into power and turn on the high performance fan profile in the HP Fan...