I have good news and bad news.....
The bad news is that unless you are a veteran and eligible for a VA loan, you are going to be paying MI in some way shape or form--it's just the nature of the beast. Sure some banks and lenders will offer you 100% financing and what not but it's going to be hidden in the cost (the interest rate) of your loan. It's just because of the risk in lending to someone who has no "skin in the game" or even any reserves or savings in order to be ready for necessary maintenance and repairs which are generally assumed to be roughly 15% of your monthly payment.
The good news is that even with whatever 'offers' are available from lenders today---whether it's a Lender Paid MI (LPMI), a HUD home you buy with $100 down, USDA (which has Guarantee Fee), a National or your local Credit Union---rates are so low that it even makes the MI affordable.
Nonetheless, you ought to reach out to your local non-profit home ownership center to see what's available. There are lots and lots of DPAs (down payment assistance) programs that may be good options to help you get started.
However, you will also want to be sure that you are saving for your retirement as well. When the time comes to apply/qualify for that mortgage loan, a bank would really like to see that you have money set aside for retirement and most plans will allow you to borrow from them which can really come in handy as life happens.
I suggest interviewing 2-3 Realtors, explain your situation, and ask them if the mortgage lenders they work with will be able to assist you in the type of program you're seeking. Kill 2 birds with one stone.