Congrats @Connor Ong. Love the strategy.
I would put as little money down as possible as long as the income covers the expenses (particularly when you would move out). Lower DP decreases cash flow but increases ROI. Also, equity in a home can be difficult to access. You are better off keeping that capital for reserves and using for next investment/house hack.
Paying your student loans down would not help your DTI. DTI is based off the payment, not the outstanding balance. I have LOTS of students loans as well (double yours) and I refinanced them to a better rate and lower down payment and use the increase in cash flow to arbitrage the interest rate vs a higher investment return. This strategy is different to everyone (I don't have much of an adversity to debt). If you are a good steward of your money (sounds like you are) I wouldn't pay it off and better to invest it. If you do want to pay it off ASAP the best way to do is to save the money in an interest bearing account and they pay it off in lump sum once you can cover it all. This way you have control of the money (as opposed to making extra payments the money is gone, you can't get it back in an emergency, and it doesn't change your payment). You may pay a tiny bit more interest in the end but is worth having the control.
You should think about what your plans are with investing and long term goals. If you work backwards with the end in mind it will be easy to create a plan to meet those goals.