Can I have a 600-700 dollar house payment
All other things being equal, you can find a home that will fit your budget. As said before, it will be dependent on the location as to whether a home can be found in your price range and that the 600-700 will fit in your budget, based on lending guidelines.

Are down payment assistance programs a good idea?
As they have said; they definitely have a purpose in helping people on the lower income scale purchase a home. KS has a grant program(no repayment) to cover up to 4.5% of your down payment and closing costs. Another option for you would be to look at USDA. They offer 100% financing, there is no upcharge to the...