Maybe it's just the angle of the photos, but both of those front trees appear to overwhelm the small house. Removal of at least the right leaner is warranted, and that may take the pressure off the retaining wall for the time being. You would be amazed by how a simple neatening up and trim job can make a huge difference in garden appearance. Raking, leveling, and mowing in the back will help. The sagging fence will need attention someday, too, but maybe isn't a priority. With budget a concern, I'd remove the big tree and hire a maintenance crew to do a one-time tidy up that you can maintain yourself afterward.

I think it works better on a forum like this if you limit the project of the thread to a single area, front yard OR back yard, or at least deal with them one at a time within the thread so as to minimize confusion. If you wanted to start with the front, you'll need to provide better pictures. As it is, none of the foundation planting area can be seen in detail. And the lighting in both pictures is very dark. To get good pictures, I would stand at the top of the yard steps and take 3 pictures all from the same position, pivoting the camera. For the first picture, aim the camera left so that the left side of the house shows up, but mainly you'll be looking at the left side of the yard and the neighbor's yard. For the next picture, aim the camera straight ahead and take a picture where the house is centered. For the third picture, aim the camera right so that the right edge of the house shows up and you'll be seeing the right portion of the yard and the right-hand neighbor's yard. The pictures should overlap some. Hold the camera level for all three pics.

As your yard is divided into levels, I would take a second set of 3 pictures (in the same manner as the first) but move back so that the camera position is about at the curb.

Keep in mind that landscaping deals as much with what it beyond your property lines as it does with what is within them. While you will only build and plant within your yard, you may be doing it to screen out something ugly that lies beyond your yard. We wouldn't know what's there until you show it to us.

I would start with removing at least one of those trees, and then fix the retaining wall. They're the big ticket items, and once they're done, you can start planning out what you want to do with the rest of the yard. And you can probably take the shed down by yourself--the foundation, etc. may require help............

http://www.hallslandscapers.com

Do nothing in haste! If the tree is dangerous, sure, take it down. But hold off on the shed. You may find you need a shed as much as the previous owner did, and will learn how expensive they can be. The one you have (which I can't really see) could be a charming feature if painted and planted. Just wait. Take your first year to take inventory of what you have - every plant, including every weed, your sunlight and views. Landscaping is such a combination of patience and urgency. Urgency to plant things that will take so long to grow. Urgency to do the fast jobs because there are so few that are fast. But patience in both cases is rewarded.

Before you start cutting down trees, contact an arborist. The trees overwhelm the house because neither has been trimmed in years, and by trimmed I mean taking the canopy up. If the tree is diseased or dead, then by all means take it down. But you will regret removing trees when summer hits and your AC bill is through the roof. And run from any arborist who attempts to "top" your trees - as no legit arborist would hack and destroy a tree by "topping it." I don't know why any sane person would tell someone to take down those lovely shade trees - it takes 50 years of growth to get trees that lovely. And those trees mean VALUE to your house and taking them out will reduce the value of your house by 30% - don't believe me - talk to a Realtor or your insurance agent.