Re: the hedges, a lot depends on the species. Some hedges will rejuvinate following trimming - others will leaf only on new wood. Also, the species will dictate how easy they are to remove. Many have small shallow root systems, and most evergreens are pretty soft wood. Depending on what you want to do with the area afterwards, you can often get away with digging around it, simply lopping off the aboveground growth, and sawing/axing the main stem(s) a few inches below ground level. Maybe paint the exposed wood with Roundup to dissuade suckers.
The first thing you are going to want to think about is what you want to do about trees/bushes, as they will in large part be the “bones” of your yard, and take the longest to get established and mature. If you are going to tear out the mulberries (I’m not a big fan) you might want to have it done before you install too much hardscape and plant material.
You might benefit from having a landscape designer take a look and draw up a plan. Some guys/companies will do a plan for a flat fee of a couple hundredd bucks. Often if you hire them to install at least a part of it, they will comp the cost of the plans. Just saying it might help to see it through neutral and experienced eyes. Walk around and see yards you like, and ask those folks if they had anyone help them. If you see someone out working in their yard, they are often happy to talk about it.
Whether you ask a pro or DIY, you will need to think of how you will use it. Think along the lines of creating different “rooms” outside to expand your effective living space. If you want to cook outside, you will need a food prep/kitchen area - probably near the door to the inside kitchen, but not blocking a main traffic pattern. You might want a seating area for guests, which could be a deck or patio. You’ll want to have sufficient shade and privacy. You may also want a play/recreation area, space for pet exercise, flower and vegetable gardens… What views do you want to emphasize/hide, from both inside and outside the house? How much time/effort do you want to put into ongoing maintenance?
Just saying, ending up with the yard you want takes considerable more planning than just digging a few holes and dropping in a few plants.
You’ll need to buy a few tools: shovel(s), spade, hose, rake(s), loppers, pruning shears, etc. Do a little research buying, and start with the basics before getting fancy. Garden tools get pretty hard use; you’ll do well to buy decent quality stuff.
Another thing, starting from a pretty bare canvas, you will never be in as good a position to amend your soil. You might want to check with local garden centers, community colleges, farm extension bureau, etc. to find out what the soil is like in your yard, and what would be best to amend it. Depending on what you’ve got, you might want to add manure or something else.
Oh yeah - take plenty of before and after pictures!