Like with anything else that matters a lot, you should consult a professional when you're ready. I will just add to the comments below that while the length of the employment is very important, so too is the TYPE (hourly, salary, self-employed, etc.) of employment. You have provided a lot of good information above, but none of us could give you the certainty you seek because we simply don't know enough to make an accurate determination of whether or not you'd qualify.
If you would like help with this in the future, and on your terms, please keep me in mind and I look forward to being of service then.
First, if you've worked in the same field of work for over two years, then you show consistency in employment. With the current FHA backed loans, you are required to come in with 3.5% down, with a minimum credit score of 620. Those two are the black and white requirements.
Your first step is to meet with a lender, have your credit score pulled and see where you are. If you are not high enough in your credit score, they can help you make a plan on how to improve it. If you haven't got the savings for the minimal downpayment, you'd need to make a plan to save it, or possibly borrow it from family members. Yes, there are some special programs that help for low income families, but these are not common so I'd start looking at qualifying as a general first time homebuyer first, THEN understand the nuances of other assistance programs that you might be able to take advantage of.
So you're over 720 you qualify there. And can you come up with a minimum of 7K? Your payment on a 200K purchase will average around $1200/month including principal, interest, taxes and insurance. You seem to be well within the debt to income ratio to qualify for a $200K purchase....but the lender will look specifically at all of your spending, assets, income etc. and be able to speak specifically for you. Cal Mark Holmes at (916) 837-4360. He's with American Pacific Mortgage and can help...lots of information at no charge and very trustworthy and helping alot of my first time homebuyers.
It has programs to help first time homebuyers with the down payment and good 30-yr fixed rate loan programs.
You both will need to attend a first time home buyer education class which will provide you with a certificate to qualify for the programs described above: http://calhfa.org/homebuyer/information/index.htm
Good luck to you both, have fun looking for your home and let me know if you would like more information.