I might be the only one saying this, but I wholeheartedly agree with the landscaper who refused to cut everything down. Give yourself time in the property to get to know the plants, trees, shrubs and any flowers growing. I think you'll be amazed at how maintenance-free many of them can be. It would take 20 years to get taller trees again if you change your mind.
I would try talking to your neighbors again. Explain that you're new to gardening and would love any insight they have about the existing trees and shrubs. They might be more willing to open up if they realize you're not going to raze everything to the ground.
And from your neighbors' perspectives, I'll also add that when my neighbor had to move 2 summers ago (that I absolutely loved living next to, we still keep in touch and visit), the new owners came in and within a month cut down everything in the front and back. This includes 20 year old rows of beautiful peonies, daylilies, a lilac bush in the back, a row of 8 alpine currants between my driveway and their house, and all front evergreens planted around the foundation. There are 2 trees left, only because the back one is too large for them to cut down without costing an arm and a leg, and the front one is on the parkway, owned by the city. I'm on friendly terms with the new neighbors and will stay that way, but I'll never be close to them. I get a horrible feeling every time I look at their yard, reminded of what was there. Nothing was planted in place of what they removed, so there are just wide swaths of dried dirt and weeds all summer that they don't take care of. It's depressing to look at.
Don't be that neighbor. Yes, it's your property, but at least have a plan if you want to change the landscaping and not just tear everything up without knowing what's there and what you want.
