Sunny and shade ground covers

As at least some of you know I have been growing and showing daffodils and iris grown on a relativity small city lot for 30 years.  I have always been a plant person and not a yard person.  I would not at presently invite any of you to visit my yard. 

Now that I am retired I want to rectify that. 

I have two Eco systems as my house faces south in the very hot delta city of West Memphis, AR.  My bloom season is 10 days to 3 weeks earlier than that of Memphis, Tn which sits on a bluff.  The front yard receives a great deal of sun.  The backyard has two large pin oaks.  The bloom is later in the backyard.  The front yard is still 2/3 grass with weeds.  The backyard is mostly weeds.

My request is for information as to what kind of ground cover can be used in each Eco system that will permit daffodils to grow through them. 

Jim Russell