I would live with the property as is for a few months before removing anything. Give it a good walk about and then decide what you want to take out and what you might like to leave. If vegetable gardening and a full on flower garden is what you're after lots of the shade producing trees will have to go. But there's nothing wrong with having the best of both. I love a shade garden with ferns and hostas and hydrangeas. You can keep some of the trees and create a shady nook to enjoy on a steamy hot afternoon. At the same time open up another area for vegetable and flower growing or perhaps some manicured shrub beds with a lawn. This is YOUR space now. Don't let other people run your show. Make it what you want. Good luck and Welcome to NGA!