If we got our current house with a VA loan and have lived in it for a year-and-a-half (since refi) , I believe that satisfies the primary residence requirement . Could we now rent it out and buy a new house using remaining VA entitlement and having the rest on an fha loan? We would be living in the new house. And then what would be the options for pulling out equity of the now rental house?
Or could we pull out the equity first without restarting the occupancy requirement?
You can't combine 2 different products. You can either go FHA or VA. If you don't have enough eligibility left and cash to pay the difference than you would have to go conventional or FHA.
You can get a HELOC on the property prior to moving out, while it is still your primary residence, but once it is a rental property, you will have to abide by the cash out terms of an investment property.