Advice for a prospective grad student

[lpenn22]

Hello,

I'm currently an undergrad student looking for advice. The below information is based on what I've done/what I expect to have done by graduation.

Undergraduate Institution: Decent US State school with a solid statistics department but not particularly known for math. Ranked around 50 according to US News
Major: Math and Economics
GPA: 4.0
Math GPA: 4.0
Type of Student: Domestic white male (first gen if that matters at all)

Classes taken/to take:
Undergrad: Calc 1-3, linear algebra 1-2, proofs, ODE, PDE, numerical analysis 1-2, probability, stochastic processes, machine learning, real analysis 1-2, complex variables, introductory statistics, mathematical statistics 1-2, intro programming, python for economics, game theory, R for economics, intermediate micro/macro, financial econometrics
Grad: Real analysis 1-2, Econometrics 1-2
GRE Not taken (maybe I will but not decided yet)

Research: I'm planning on applying for REUs this summer focusing on something along the lines of financial math and probability.
Idk if this counts but I also plan on doing directed reading classes for the upcoming semesters, been looking into topics recently.

Programs applying to: Applied Math, Statistics, Operations Research

With all this in mind my questions are:
1. Around what rank should I be aiming for?
2. What can I do to improve my profile?
3. Are programs in applied math/stats/OR less competitive generally than those for pure math?
4. Since I'll be lacking heavily on research would it be worthwhile to do a thesis based masters before applying?

Thanks

[juicetrainwreck]

1) apply to whatever school you want, don't be concerned about ranking. College is what you make it

2) gre could be helpful. Some real life experience like work could be beneficial too

3) idk

4) that would probably help