Will having parent cosign keep my credit free for more deals?

[Derek B.]

Me: great W-2 income, excellent credit, practically 0 debt, plenty of savings, west coast. 

Mom: fixed income, retired, renter, worried about rent increasing, east coast. 

While looking for my first RE investment, my mom presented this problem. (We are problem solvers here amiright?) So now I'm looking for a small multifamily for her to house hack. I'll be paying the down payment and she will be paying some of the mortgage which would significantly lower and stabilize her monthly housing cost.

Question 1: Will her cosigning on the mortgage look better on paper to future lenders for my future real estate investments? It will be her primary residence after all. Now that I think about it, I think she will need to cosign so I get the best mortgage rate because of that. 

Question 2: Is it a better option for my future deals to just gift her the down payment and have her do the mortgage herself?

Question 3: If the mortgage is in my name, what is my best type of loan. I can pay 20% or more down, but I'd like to keep my capital free for future deals. What are the ballpark trade-offs based on current rates if I put less down? I'm eligible for a VA loan, but I don't think the property is eligible because of occupancy rules. I love my mom but I'm not moving in.