To answer your specific question, I think you and your wife are strong candidates for a mortgage and I do think an FHA loan is likely your best option given your credit scores but there are several factors you should consider when you apply for a mortgage.
First, applying for a mortgage as a self-employed borrower is different than applying for a mortgage with a typical job. If you are self-employed, such as if you own a business, lenders usually use your average monthly income for the prior two years to determine what size mortgage you can afford. So if your business' income was significantly lower last year than this year, then the income figure the lender uses to determine what size mortgage you qualify for will be lower than your current monthly income because the lender uses a two year average. Using a lower income figure results in qualifying for a lower mortgage amount.
Additionally, most lenders require self-employed borrowers to provide two years of business tax returns. We provide a comprehensive explanation of How to Get a Mortgage If You are Self-Employed on FREEandCLEAR for you to review. In short, getting a mortgage if you are self-employed is certainly possible but it requires some extra work by borrowers and additional documentation.
The second point you should consider is the legal ownership status of your property. Depending on how the property transfer was structured and recorded you may be looking to refinance an existing mortgage or your mortgage request will be treated as a home purchase loan. If the property seller transferred the property to you using a recorded grant deed and the seller legally recorded the seller loan with a deed trust or mortgage note then the mortgage you are seeking today would refinance the existing seller loan on the property. If you do not hold legal title through a recorded grant deed and the seller loan was not recorded then your mortgage request will be treated as a home purchase loan.
Although the processes for a mortgage refinance and home purchase mortgage are relatively similar, there are some differences when it comes to your required down payment. With a refinance, lenders focus on your loan size to the value of your property (loan-to-value (LTV) ratio) so your down payment is not relevant.
In the case of a home purchase loan, lenders require that borrowers make a down payment (3.5% in the case of an FHA loan) so you will be required to provide documentation to verify any down payment you made to the seller. It is also helpful to verify that you have paid down a portion of the seller loan through your monthly payments as your principal reduction is also considered a down payment.
You should be fine regardless of if your mortgage is classified as a refinance or home purchase loan but it is helpful to understand the difference between the two.
The third point I want to address is your tax payments. Unless your tax debt is structured as lien against your home (which is unlikely) then your tax payments are the same as any other monthly debt payment such as a credit card bill or car loan. Given your relatively low monthly debt expense as compared to your monthly gross income, you should also be fine on this point. We review mortgage qualification guidelines including debt-to-income ratio and credit score requirements on FREEandCLEAR.
Finally, as you referenced in your question, the FHA Mortgage Program is likely your best financing option given your credit scores. The FHA program enables you to qualify for a mortgage with a credit score as low as 580 and potentially lower in certain cases. The other program you may want to consider is the HomeReady Mortgage Program. The HomeReady Program is similar to the FHA Program but it is a conventional program, does not require an up-front FHA mortgage insurance fee but does require a higher credit score of 620. We provide a thorough overview of the FHA Mortgage Program as well as an FHA Mortgage Qualification Calculator that enables you to determine what size mortgage you can afford based on your monthly gross income and debt.
After reviewing the resources on FREEandCLEAR we recommend that you contact multiple lenders to understand how they would handle your unique situation. You can review lenders in your area by clicking INTEREST RATES We advise you to contact at least four lenders as qualification guidelines vary. Plus, comparing lenders is the best way to save money on your mortgage.