buy my house 100% or finance?

so i saved up $1,200,000.00

i want to rent out houses.

with months of research i learned it is cheaper to buy out a house than it is to finance (no closing costs or APR as told by my financial advisor)

so i figured I'll do that. now the only thing i want to ask is i need to buy my own home to live in. should i just buy a house out? or since i live here would i finance it?

i am a veteran so i do not have to pay closing cost on my own home. and i get a decent APR and no money down. but i can only finance one house using that.

average house i want to buy for renting is $180,000. (granted paying in cash i can robably talk them down to $167,000-$170,000)

my house is around $240,000

reason why i am asking is should i finance my house, sabe the extra cash and use it to buy another home outright to rent out?

quick example: if i rent out 2 houses and buy out my own home I'll be about out of investing money.

if i finance my own home i will be able to buy out 3 houses and rent them out.

only thing i can think of is as long as my mortgage is less than the 3rd house's rent I'll make a profit by financing my house. any thoughts?