Relocating from LA to Nashville, loan options for primary home?

[David VanWert]

Currently live in Los Angeles and gearing up to relocate to Nashville early next year. We will be selling our primary home here and purchasing a new home around Feb/March next year. 

We should hopefully net $700-800K from our primary and are looking at homes in the $3.5-4M range in Nashville. Would like to hopefully purchase another investment property with the sales proceeds around the same time as the move. Question is, is there 10% Jumbo loans for that amount and use the remainder for the investment property, or maybe use an AIO loan , other options I'm not thinking of? 

Looking to maximize the net proceeds and hopefully pick up our dream property and add a cash flowing property to the mix at the same time. 

Would really appreciate feedback of the best way to achieve hopefully both homes and different strategies for primary loans in todays current climate. TIA!