Where are you located? That will determine some plant choices.

We're from Keizer, Oregon

Sorry. Not familiar with that part of the world (plant-wise).
Anyone out there have knowledge in this area?

It's the Willamette Valley if that helps at all

Now can you make a shot from the fence toward your house? Do you already have a deck ? Do you have children that need space to play? What do you want from your backyard ?

If you have a budget you could take out a section of the lower portion (near the chain link) and create a leveled area with raised firepit and some chairs all on a paved patform. You look like you do winter there so go for hardy shrubs to accent the yard and along that link fence put in some dwarf evergreens that grow up and not out too much and save space for colorful annuals you can swap out in the warmer weather. Or you can just rip out all the grass on the slop3

Love the landscaping

That landscaping looks great! We would like to keep as much of the green grass as possible with a small budget. Here is some more shots of the back.

We have a big deck already

Can you make several more with the house centered in the middle ? Shoot from the fence toward the house. Its hard to get ideas from the above.

Looks like you enjoy your entertaining space. I would plant the gap between decking and chain link with either hardy bamboo ( green, height, privacy and movement) or other evergreen shrub which grows high to nestle the decking. Coming down from the decking i would create another planting space. Stagger plants medium to medium high looking from the decking and again tapering of towards the lawn area. This creates a sectioned area for your decking and a distinct zone while giving you something nice too look at from the deck and the garden. Think about evergreens, fatsia japonica( fairly inexpensive, large leaves, visual interest) grasses and some climbers like jasmin for scent. Next zone around the fence build up a green hedge. Looks like your neighbours have red robin which is a good choice for evergreen, stunning colour and fairly fast growing hedge. Laburnum could be alternative but does not offer the stunning colour. Again plants are fair for the budget. Lastly I would round of the planing with another bulk planting zone at the far end of the garden. Opposite the decking. Create another sitting area which gives you an alternative view of garden and house and a place you can enjoy a view of the plant area and fairly lights on the tree from. Maybe an arbour or bench with evergreens and scented climbers.

Here are some more photos. Thank you for the suggestions so far. The ideas are starting to flow.

If its important to you the first thing I would do is invest in a nice fence to surround the entire property -the existing fences look pretty bad. What are your needs for a backyard ?

If you want to maximize the yard....you need a retaining wall to level out the yard. If you want to keep the slope as is you could use tall ornamental grasses to gain privacy as well as handle run off. I personally vote retaining wall. Here are a couple of pictures to get ideas. If you want to browse more ideas go to www.blushirt.com

I could potentially see a tiered space here.

A suggestion of grass would be Miscanthus gigantica