If Conventional, the rental income won't be counted unless you have a history of prior investment property management.

If FHA, the income will likely be counted, but per HUD:

"3-4 units must be self-sufficient

• Maximum mortgage is limited so that the ratio of the monthly mortgage payment, divided by the monthly net rental income, does not exceed 100%"

Which means you have to live in one, as you noted, the remaining units must be "self sufficient" and your down payment might have to be increased depending on the cash flow.

Thanks for reading,

LoansbyJW