Looks like a nice house! You might want to consider cross posting this on either the trees, perennials or shrubs forums depending on where you would most like to go with this... or even the garden design forum.... the Pennsylvania gardening forum is kinda slow for the last year or so. First thing, you don't necessarily have to keep all your plants against the house, a small tree might work if it's planted 7-8 feet out from the house and you keep an access path between it and the wall of the house. As it grows, trim it up so you can get by. Some possibilities might be a tree sized magnolia, sourwood, heptacodium, kousa dogwood, american dogwood, crape myrtle (check hardiness), a taller/narrow crabapple.... maybe an arborvitae if you want evergreen. Keep the root ball of whatever you plant slightly above soil level so that it won't drown in the clay.... and give it a nice muich that will break down and lighten up the soil. You might want to consider some tall ornamental grasses to fill in the yard while other slower things catch up. A nice grouping of miscanthus or feather reed grass might help anchor the house into your lot. I've got more ideas, but that's something to get other ideas flowing!

Air sealing is your fastest savings. You might consider hiring some one to blower door test your house and make recomendations about where & how to seal the leakage. Some companies will also test the ductwork. fix the house leakage, repair the duct leakage and see if utility cost does not go down. You could prolly find a lot of the leakage sites yourself if you know what to look for. (wish I knew how to put pics in my reply!) Spiders build webs were air moves. Look in cabinets by plumbing penetrations, inside closets, ceiling moldings, light fixtures. Most areas inside your house are best sealed with caulk which will expand and contract with the house. Open your return air..do you see exposed 2xs'? If you have a heating system closet look around the door frame..dust? can you shine a flashlight and see the return air plenum? do you see dirty insulation in the r/a? Is the platform sealed to the walls & to the door when it closes? If you really want to do some homework..go in your attic. Look for spiderwebs and dirty insulation. where there is a gap or a hole or even an open plumbing wall the insulation will be dirty around the opening. This is where the house sucks dirty insulated laded air into your house. Are the supply and return plenums well sealed to the heating system? Duct tapes fail, foil tapes don't adhere well..these are areas to be mastic sealed. take a look at the ductwork..again..dirty insulation? move the insulation back at the duct to duct collar connection at the supply plenum. Is it mastic sealed? are there areas of the living space open to the attic? over shower units, around chimney? you should have a good air barrier first, then a good insulation barrier. btw, where are you located? best of luck.

Solid roof patio cover will give the best shade although more costly than a flat open beam structure with say shade screen over the rafters. Depends on whether you want full shade or filtered sun. Make it big enough (12x12) so it actually functions. Design it around what you are going to put under it, i.e. a sit around table and chairs? Just chairs? Remember the sun angles change during the year with the best shade in June midday directly below the cover. Other times of the year and during the day, the sun will penetrate below the line of the cover. You can always put retractable shades on the west facing side if you tend to use it late afternoon. Why build a patio cover if it only provides a little bit of shade? A solid roof patio structure (gazebo or ramada) must be designed to handle the snow load and be pitched sufficiently for runoff. Plus you say you get high winds, so the posts must be braced to withstand the wind. See if you need a building permit for a free standing patio cover before you start to design it. I am not a big fan of using trees as the only solution when people say they want shade. Do you want to wait a few years before you will get any kind of useful shade? Build the patio cover and then plant shade trees on the south and west sides of the structure to help with different sun angles.

That looks a lot like a Camellia (maybe C. sasanqua?) to me. Has it ever bloomed? It may not that far south. If that's what it is, it's evergreen and doesn't get huge, maybe 10-12 feet. I'd find out for sure before I take them out. They don't have invasive roots, so they won't hurt the foundation or grow up into the house. Even if they don't ever bloom, they are beautiful evergreen shrubs. I'm not good at landscaping, so I have no other recommendations.