What kind of FHA lender approval can I apply for?

Mortgage Brokers do not need to be approved.
Obtain Sponsorship from an FHA Approved Lender

Mortgage Lenders, Mortgage Bankers and Correspondent Lenders can apply to be a:
Nonsupervised Mortgagee
Investing Mortgagee

Banks, Savings & Loans can apply to be a:
Supervised Mortgagee
Investing Mortgagee

Local, State and Federal Agencies can apply to be a:
Government Mortgagee
Investing Mortgagee

All Mortgagee approvals (except Investing) allow the lender to originate, underwrite, service and holds Title II Single Family, Title II Multifamily and/or Title I loans.

If you want to apply for both Title II and Title I loan programs, you will receive two FHA Lender ID numbers, one for Title II and a second for Title I

FHA Loan Programs:
Title II Single Family (203b, 203k Rehab, 234c Condo, HECM Reverse Mortgage)
Title II Multifamily (Rental Housing, Nursing Homes and Hospitals.)
Title I (Manufactured Home and Property Improvement Loans