Two suggestions - consider investing in a landscape design. Having a professional walk the property and look at all the factors (e.g., drainage patterns, sun/shade patterns) and evaluate your landscaping goals, etc. can be well worth the price of the plan ($200-400). This could save you a lot of planting mistakes, wasted effort and help you see some issues that no one on the internet will be able to spot.

Also consider incorporating some native plants into your design/choices. Especially on the fringes of your wooded areas to create a more natural transition. Plus native plants support the ecosystem that you're moving into and attract the natural insects and birds that your kids would love to observe as they play outside (I'm not talking about biting, stinging insects - you'll get those no matter what you plant; these are caterpillars and butterflies and moths that will be attracted - think Monarch butterflies that only eat milkweed, same concept). Also problem areas like poor drainage and wet sloping areas to a low area have perfect native plant solutions and believe me that willow is not the only one. Native plants can be beautiful, have flowers, great fall color and be treated just like non-native plants in a landscape.

As far as planting next to the property line, remember that anything that hangs over the line can be trimmed by your neighbor (the part that is on his property, that is). Research the mature width of a plant and then divide that number by 2 to get the distance from any line or wall for planting.

Recognize that the weather is warming up and that anything you plant now will need to be watered through the summer - fall is the best time to plant trees and shrubs. Get a plan now, plant only as much as you feel you can keep up with with, mulch well to retain water and suppress weeds, and plant a lot of annuals this year to enjoy while you get ready for fall. In the meantime, research your desired plants so that you know what you're getting. Even with a plan you may not like everything that the designer chose - I swapped out a few things on mine for plants that liked the same conditions. A plan helped me feel like I had a roadmap and I was able to implement it as my finances and energy allowed.

Taterville,
Congrats on your new home!
It's hard to buy a new built home and have all that landscaping to do, but don't panic, it will take you uears to get it the way you want it, and then you will change it again. LOL!
Start out simple. Yes, Butterfly bushes do well and provide privacy, just remember,
Cow manure compost
Mulch
and you will be fine!
Buy alot of the two above mentioned things!
You can plant right up to the property line if you want.
You can install a privacy fence also, even just for a small portion of your property for now, for the summer.
If there are too many rocks, tell hubby not to mow, he is also creating a danger to people.(not to mention he will need a new lawn mower).
Some shrubs to consider,
Butterfly bushes, Green Giant arborvitae, Leyland cypress, Sweet Olive trees, Roses, (they can get big, and bloom real well in the summer),
you will have fun with this.
As far as the drainage out back not being that good, you will have to ask around, it sounds as if you need a way to get it to run down the hill away from where it is puddling.
I'm surprised a little bit the builder wouldn't have caught that, and get a couple of rain barrels to catch some of that expensive water from your rooof for your plants.
I bought one at a big box store, but it never rained.
Good luck to you and your new home, I am happy for you.
Plant some Butterfly bushes and enjoy all the butterflies this summer.

I second the cow manure suggestion. It sounds like you are out in the country at least a little. Red clay appears to be very difficult but it holds water and nutrients superbly. Adding cow manure (bedding and poop) or something else will do the trick, but you need truck loads, not bags full. Fortunately you are proabably close to a farm that will load up some manure into someone's dump truck. With gas prices up again, that might be around $150. When gas was $1.70 I found a cattle farm charging $50 a load, and it was $60 for 20 mile delivery. That was for approx 15-20 cu yds. There are always commercial places that will do the same for $300 or whatever.

esh ga- thanks for the awesome tips. I found someone giving free aguja that we are going to plant at the bottom of the front hill-should be a great native ground cover.

butterfly4u-I'm glad butterfly bushes do well. I didn't see any at the farmers market this weekend but I did see a knock out rose tree and I'm in love. At $25 a pop I'm shopping around but we have one rose bush that is doing great in front of our house. The sweet olive trees are really pretty too.

chas045- I am near plenty of horse farms, will have to check out to see if there are cows too. Do I put the manure on top of grass?

I found a useful site listing plants that tolerate wet spots.

Ajuga is native to Europe and western Asia but not the United States.

Here is a link that might be useful: Qualifiers for Quagmires

The trick on the manure is price, convenience, and weeds. I'm just guessing, but I suspect cow manure has more bedding mixed in it which is a good thing under the circumstances but horse is great too. If the stuff is piled up somewhere on a farm, the local weeds may come along with the manure. If these weed are not already in your yard you might not want to introduce them? However, a nice hot composting pile of manure may have killed the weeds inside the pile. And the biggest part is the farm needs a loader or something to scoop the stuff into your pickup or into someone's dump truck. The dump truck route is double good because loading and unloading are taken care of. The pickup can be convenient though if you can drive it around to different spots and rake stuff off the back.

But that gets us to the big toys. Bring in dump trucks full. Let um sit a spell until they cool down if not already aged. Then hire or rent a skeed steer (Bobcat) to relevel non draining areas and spread manure over lawn and landscape area and move big rocks around etc.