Which internship should I choose this year to help me land an internship at big quant fund next year

Hello,
To give background: I go to a top five school in the country which Two Sigma, DE Shaw, AQR, Bridgewater, Citadel, etc. recruit heavily at. I want to work at one of these larger hedge funds that have more technical sides.

This summer, I was not able to get any internships at those companies. However, I was able to get offer from a MS in a rotational fixed income S&T, a mid-tier bank's data team (they use a bunch of alternative data and machine learning to give insights to research analysts.), and a ~100Bill AUM asset manager that is a quant shop. I think I will be doing investment related research there. However, no one has heard of this quant shop and their performance is nothing special.

I feel like I should not consider pay for this internship, and should think about what will help me make more in the future.

I am wondering what I should take. I assume it would make little sense to do MS FI S&T, even if it pays more. I feel like data shop and quant asset manager would be better choices. What do you think I should take?

I assume I want to make sure I have a technical internship that is research related, no?

I have to decide if I should take MS today. Should I turn it down?