Possible to get my PhD after my master? so Johns Hopkins or UW?

[eastVillageWest]

Hey guys! As the title is saying, I want to pursue my PhD in PDE or ML after my master and i'm going to pursue my master soon after I graduate from my college, but i don't know how to be prepared to apply in fall 2020. So a little about myself first, I'm at my senior year majoring in Financial Mathematics at a public university in NYC (GPA: 3.8); A/A- at my math classes, and took two graduate level math class; I won some national trading competitions (cause I wanted to do quant research before... ); currently doing some Deep learning/PDE research work with a professor.

I planned to do QR right after my graduation, but my passion for pure math won. But as you may realize, it's a bit difficult for me to apply to PhD last fall (I didn't have any research experience or any conference/presentation... ), and as my professor suggested, I applied for some math programs offering master degree to get some research experience. I recently heard back from Johns Hopkins Financial Mathematics program, they will provide me 25% scholarship, and also UW at Seattle for CFRM.

I know my background is not strong at all. But I do want to pursue my PhD at NYU Courant/MIT/Stanford/Berkeley (almost all my math professors are from the four, and i love them!). I just wanna know what to do during the first year of master (it's gonna be a 1.5 year program) to apply to them in 2020 fall and which school I should choose to have a better edge.

As my professors are saying, UW has a very good applied math department and J.Nathan Kutz is pretty good at DL; but i guess Johns Hopkins has a bit better stats department (they rank almost the same for that...) and a better name (i guess?). I do hope the program I choose goes hard on math proofs and have better way to provide opportunity for PhD path.

I'd love to hear all of your ideas! Thanks in advance.