Since you are travel nurses, I am guessing you are paid 1099. There are still options for you. There are many lending options to proceed:
1. DSCR loans: Your personal income is not used as proof of income. Rather if the property monthly rental income can cover the monthly Principal and income, taxes and insurance, and sometimes HOA fees(PITIA). You get qualified usually based on credit and DSCR ratio, with other lender specific requirements.
DSCR ratio= Monthly rent/PITIA. Usually a ratio of 1 and above is good. 1.2 and above with a 660+ FICO will get you better loan pricing. Some lenders can do DSCR ratios down to 0.75 but note your loan pricing will be crazy high. DSCR loans usually have interest rates 1-2% higher than residential interest rates. Keep in mind it is possible to buy down your rate usually 2-3% as long as that does not fail the points and fees test. Ask a lender about that.
DSCRs will usually be used for if the property already has tenants and is cashflowing. Some lenders will lend based on estimated rent but your pricing will be higher. This loan is not used for rehab. Can be used for purchase, refinance, cashout refinance.
2. Bank Statement loans: Even better, and will get you better pricing than DSCR loans because you show proof of income, meaning lesser risk to lenders. Lenders will usually qualify you based on your Bank statements for usually 6 mos -2 years. Check with lender for pricing. Even better for self-employed 1099 workers
3. 1099 income loans: Like bank statement but your 1099 income documents will be used to assess risk and qualify you.
4. FHA loans like you said are possible but get a lender to check FHA guidelines for self employed/1099 income earners before you proceed.
5. Hard money/private money to buy property and do some rehab. Once rehab done and property is fixed, you can refinance to either a DSCR refinance or bank statement refinance to get lower and reasonable monthly payments on property. For DSCR once property is cash flowing you won't have to show income just rental income vs PITIA.