There are a couple of roadblocks you could possibly have. Your credit scores should be acceptable, if your mid scores are still around 660 or 680 you have a good chance of going conventional depending on what your down payment will be. Lack of down payment and less than 2 years employment are going to be your issues (depending on the type of loan that you are wanting/needing). You might have to go FHA just depending on your lack of down payment. We just are going through the process and we went conventional, and we had to have a certain amount in our bank accounts or they wouldn't have even entertained the idea of approving our loan.
Just my 2 cents. I know it is hard to kind of make up your mind that you are on the road to wanting to buy a home, but you must ensure that you are doing the right thing for your family in creating a solid financial future. Just don't get ahead of yourself, it is just easier going through the process if you have all of your ducks in a row. Things always come up in the loan process either way, but I can tell you from experience if you have to wait a couple more years to get some savings in the bank, that shows a lot of diligence and you will be better in the process for it.
Also, it isn't just the purchase of the actual home... There are other costs that add up (furniture, appliances, closing costs, etc.) So, if you feel like you don't have a lot of money in the bank I would just keep saving and purchase a home when you have a little more flexibility with your accounts because it is extremely expensive.
Starting Score: 600