Lenders look primarily at 3 things when approving you for a mortgage: Income, Credit, and Down Payment.
Income - not only the amount you make but how long you have been at it. Consistency is important. Over 2 years at your current job will help
Credit - Your scores can help determine what interest rate you get, but more importantly lenders look at your credit profile/payment history to determine if you are a good credit risk. A 640 credit score should be workable, but that is towards the low end and you would do yourself a service if you got those scores up before you bought.
Down payment - FHA permits you to finance a home with as little as 3.5% down. VA (if you are a qualified veteran) offers no down payment. 0% down conventional is basically a thing of the past, and even when they were available they required good credit scores.
Your challenges here are the low credit score and lack of down payment. Not to say it can't be done, but in my opinion you would be best off saving up some money and working on your credit before making the move. It will make the process much easier for you and you can get a better interest rate. You appear to have a good income, so you should be able to save up $5000-$10000 pretty quickly if you have no debts.
I preach "sustained homeownership", meaning just because someone is willing to give you a loan doesnt necessarily mean you should do it. You should make sure your finances are in good order and that you can fit the new payment within your budget comfortable. I want to set you up to succeed and not be paycheck to paycheck.
That's just one humble loan officer's opinion. Best of luck, and if I can be of any assistance please feel free to reach out!