I forgot to mention. There is also a sewage drain in the back right corner and so the yard slopes down slightly at the back. Here is the to scale layout of my yard. I've drawn in the trees as they'd be at maturity.

It's not clear to me what your goal is but to landscape. Though you stated that privacy would be nice it didn't sound essential. I would stay away from purchases until you know what you want. You aren't the first to impulse buy when it comes to plants and you won't be the last.

With a small yard, each plant (tree, shrub, etc) must be clearly thought out. Most of us would like an additional plant somewhere but ultimately we run out of room. You then have to prioritize what's important and what's not.

List what you need from your yard. Search the web for pics of landscaping that you like and determine what you like about it (lush, simple, colorful etc).

Thanks for the advise. I never really thought of things from the perspective of "list what you need from your yard". For now, we mostly use our yard to eat, for the girls to play in etc. I do want more from it though because almost the entire back of my house has windows that look out directly onto the yard (kitchen, family room). I'll have to put more thought into that before I make more purchases. I just want it to look nice (and green/lush), but not sure how to get there. I'm sure as the years go on, I'll want different things from it. Privacy, place to relax, watch birds, etc.).

I look at MANY pictures online and see lots of things I like. It almost depresses me though, because I can't figure out how to incorporate what I see into my small yard. I'm thinking of booking an appointment at the garden centre to get some advise from them too. I don't trust myself. Every thing I've planted this year, I'm now second guessing as to wether is was a good choice or not.

Shell, if I'm hearing you correctly your backyard provides you an adequate place for dining and a play area for your girls but a nice view looking out of your house was lacking.

Your neighborhood looks fairly new, where the builder came in and cleaned out the area, weeds, shrubs, and trees. It takes careful planting by you and your neighbors and years for things to mature into a more lush setting.

Until then though, you can make your yard the best you can. What you have already is fairly nice.

It's not known what your zone is but I would be inclined to purchase perhaps 2 sets of 3 columnar junipers and strategically plant them creating the greatest amount of privacy. You don't have to have complete seclusion to improve the feeling of separation from your neighbors. These wouldn't have to take up too much valuable footprint of your yard.

I often use showoff.com which is a free online tool in which you can load a picture and play around with tree, shrub, flower placement. It has it's limitations but does provide you with a reasonable picture of what it may feel like having any tree, shrub or flowers in that location.

Good landscaping and gardening takes patience. The best thing you can do to hurry that along, is to plant with purpose so the plant stays where it will and to fertilize properly to encourage the greatest growth.