It looks like you'll have plenty of sun, which is great for flowers and vegetables.  The locust roots will decompose in the ground, but you could clip them off at the ground to get rid of the unsightly appearance.  Your tulip tree will grow relatively quickly and provide some shade, but not much for awhile.  As you select other native trees, you'll want to consider how long they take to grow to maturity.  I'm not sure from your question if you want any lawn at all, or are looking primarily to have a mix of flowers and perhaps vegetables.  You can also consider native flowering shrubs.  If you decide to plant a seed mix from OPN, the ideal time to plant is now as opposed to the Spring.  However, you can plant in the Spring.  The key is to be sure you have minimal weeds competing with the new plants. From your photos, it looks like you have a clean slate to design your ideal space.  It would be worthwhile getting some soil samples so you know what you are working with and can appropriately amend the soil if needed.  Since you are wanting a cottage garden look, I recommend you visit some websites that discuss designing a cottage garden.  Please see the links below for native tree options.  Hopefully this helps, and best of luck with your new yard.  

https://woodlandstewards.osu.edu/sites/woodlands/files/imce/0013.pdf

http://www.dot.state.oh.us/Divisions/Planning/Environment/Ecological_Resources_Permits/Ecology/Documents/TechnicalGuidance/TreesList.pdf