Ooooooooooooo...so much potential! :-)
It will be a lot of work, but think how beautiful it's going to be when your done. The space you have to work with looks great, almost like your landscaping spaces are already set for you!
I did lasagna beds for the first time and I'm loving that! I'm extending four beds using the method and I created planting space around a pole with it also.
I plopped plants right in the two finished L-beds right after making them and they all seem happy.
FYI, on the "gushy" parts of your yard: Joe-Pye Weed seems to love the moisture and I get a bunch of it in bloom in the late summer-- beautiful, unreal mauvish-purplish color with dark maroon stems. And Lobelia Inflata is supposed to like a lot of moisture too.
Best wishes on your labors :-)

My last house was sod right up to the house. It was a blank canvas. I started with narrow beds around the house and a few island beds in the yard, plus flowering shrubs for privacy in strategic places. Each year I'd increase the size of the beds till I had nothing left but grass walkways!

My advice is to take it slowly, work on getting the soil right, make some room for food the first year, and protect your back and hands from damage from too much work. Don't try to do it all at once.

Have fun!

I did lasagna beds for the first time last year and I will never dig another bed as long as I live. It is the only way to go especially with heavy clay soil. I had plants that looked like they were on steroids and all the additives broke down the clay beneath. Another advantage to lasagna beds is that I had no weeds to pull this spring. My old beds that were done the backbreaking conventional way are still a mess after four years of trying to make them look decent. I will be topping them this year with lasagna. Like lblack already stated, you can plant in them as soon as you have them built.

For wet areas, lobelia cardinalis, iris, and cannas do very well.

Penny