Disclaimer: My web development company built the website for these guys, but the backend is all theirs.
These guys help you to perfect contracts, from building the forms (as complicated as you need, they do hospitals, financial services and more so yours should be a piece of cake) to sending them, sending reminders and making sure the client follows the correct funnels.
That aside: https://www.echosign.adobe.com/en/home.html
Echo sign is what we use here for our employment contracts, it's all legally binding and it's fast and easy.