Where to start? It depends on what you want to make out of it... I guess also it depends on how much work you want to do. If your patio is angled wierd you could tear up the concrete, put a better base down and repour it... I would say for the french drain it's probably a good idea to dig it up and redo it if it's now exposed... Taking out whatever plants you don't want... you have quite a bit of light, so depends what you want to get out of it, vegetables, fruits etc... Rasberries along the edge of the fence would be my choice. raised beds?

If you just want to do a better lawn, probably aerate the soil, and mix in some good organic matter and reseed...

Thanks ocelaris6, I just want a lawn. I am renting this property to my son and friends in August and they won't be doing any gardening I'm sure. You are right about the patio. It is in 5 1/2 rectangular shape slabs and the one closest to the basement door is lower than the one in front. My son thinks the tree nearest the front of the patio has roots pushing it up. He would love a nice level patio out there so they could play basketball on it, but he would also like a nice level, dry lawn for whiffle all. And kicking around a soccer ball. They are in early 20's but still enjoy backyard sports. He grew up here and remembers all the games they had out back. The middle of the yard is a swamp/ pond with any rain because the neighborhood slopes down and our yard is the lowest point ( we also had an above ground pool in that area so more digging was done. I know the soil is sandy with clay under it so I don't know if aerating would help or not. The more I read, the more I realize I have to build up the soil level. But drainage and erosion need to be addresses first. The soil I have has obviously been washing down the yards since the French drain is now exposed. I need a plan, as well as a way to keep the improvements I make in place.

Thanks ocelaris6, I just want a lawn. I am renting this property to my son and friends in August and they won't be doing any gardening I'm sure. You are right about the patio. It is in 5 1/2 rectangular shape slabs and the one closest to the basement door is lower than the one in front. My son thinks the tree nearest the front of the patio has roots pushing it up. He would love a nice level patio out there so they could play basketball on it, but he would also like a nice level, dry lawn for whiffle all. And kicking around a soccer ball. They are in early 20's but still enjoy backyard sports. He grew up here and remembers all the games they had out back. The middle of the yard is a swamp/ pond with any rain because the neighborhood slopes down and our yard is the lowest point ( we also had an above ground pool in that area so more digging was done. I know the soil is sandy with clay under it so I don't know if aerating would help or not. The more I read, the more I realize I have to build up the soil level. But drainage and erosion need to be addresses first. The soil I have has obviously been washing down the yards since the French drain is now exposed. I need a plan, as well as a way to keep the improvements I make in place.

Your post is an update on a previous contribution.
I suggested on that one what could be a main cause of your problem....compaction due to a pool that sat on the area that collects pooling water.

In this post you are relating everything again, what causes and probably has added to your problem...compaction.

You want a patio---that requires a level ground which you intend to build on. That screams compacted ground.

You want your son to be able to play basketball. That also suggests major amounts of foot traffic....pounding feet and bouncing balls which also contributes to compaction. Also, I suppose the net will be affixed to a post (possibly with a heavy base) which will sit on ground that is being compacted.

You want a level lawn. Before you can hope to grow grass the ground has to be fit to invite grass roots to thrive. And it cant do that in ground that wont let water drain.

I'm reminded of persons who complain about what their dog does to their ground. They want grass---but wont do anything to curb the damage done by the dog.

You are doing everything you can to prevent fixing the standing water problem. so, either live with it or stop what's causing it.
Aerate your ground and let him play basketball out on the driveway.