After she's cleared he STD and HIV test, she should be good to go.
Beyond that, I believe you're over thinking it. I am not sure what sort of 'checks' you're referencing exactly? Are you wanting to know if she will be a good mother to your kid? If she has a criminal record? Or you are simply wanting to know if all of her lies match up?
Either way, unless you're looking to jump back into another marriage, you're over thinking this whole dating thing. Once you know they are disease-free, you should be putting her to work tossing your salad and in turn you start tapping that cornhole.
