I understand your desire to buy, however, with no savngs, I really don't think this is the time for you to buy a home.
There is more to home ownership that paying the mortgage, taxes and insurance.
In a rental if something breaks,, you can call the super to fix it.
In a home, you're the one paying to have things fixed..... the plumber ... the electrician .. the roofer, etc. - they are all expensive to call in..........furnace goes - do you have the few thoushand dollars needed to replace it?
If you're not able to save money now - how tight will you be financially once you are in a home?
You seem to be in good shape as far as your credit goes, but you really need to get into the habit of saving money.
if you don't, the unexpected expenses of owning a home might put you on thin financial ice.
At the very least - pay off the credit card debt, and start saving.
Plan for this, and you can make it happen.
Sorry if this isn;t what you wanted to hear...but I think a conservative approach will be the best for you down the road.
USDA and VA loans do not require any down payment and you can get up to 6% of the sale price in seller concessions which may possible be enough to pay your remaining closing costs. How ever unless your a military veteran or the home of interest is in a deemed rural area and you do not make above a certain income you won't qualify for either VA or USDA financing.
That said, with your score you could go CONV and put down as little a 5% and get up to 3% in seller concessions. Or, better yet, you could go FHA and put down as little as 3.5% and still get up to 6% in seller concessions.