What type of spider is this?
That is a photo of a very healthy and happy Cross Orbweaver Spider, Araneus diadematus. They are considered to be not harmful to humans. According to this article, it's not a native spider to the US, but it's commonly found throughout the country: http://naturemappingfoundation.org/natmap/facts/cross_spider_712.html .
If you can collect her and toss her outside to capture flying insects, please do so. Otherwise, I wouldn't worry too much about them.