Yes if you don' want the fruit for eating then a fruitless weeping one would certainly solve the staining problem.

Mulberries will certainly be visited by your "woodland visitors" so that will be a challenge. There is a white mulberry that is quite delicious and does not stain. Dave Wilson nursery produces them. You can find nurseries that have Dave Wilson stock in most cities and online.
I have been trying to get my wife to agree to a fruiting mulberry but they are messy and you will likely find seedlings in your lawn and everywhere else too. They sure are yummy though!

I have Illinois Everbearing in 2nd season that gets afternoon shade. Hoping I will get to taste the fruit this year. : )

Hi,
Thanks for all the feedback! It sounds like they're yummy but spread quickly?
Will my neighbors hate me if I get one?
Are thornless blackberries a better option?

Well, depends on the neighbors. If they are the kind to eat the ones on the branch that hangs over into their yard, they may be more understanding. but yep, they can be a problem.
blackberries will spread too though, both underground root runners and from seeds, so they can invade the neighbors too.
I'd give the mulberry a try. I know people who have won their neighbors by sharing the fruit. Every kid in the neighborhood will know where the tree is too.

White mulberry (Morus alba L., a Chinese native) is an invasive species in North America. According to Sylvan Ramsey Kaufman and Wallace Kaufman (Invasive Plants, Stackpole Books, 2007), "white mulberry is considered a severe threat to the red mulberry (note: a native tree), particular in Canada where red mulberry is uncommon. White mulberry pollen appears to overwhelm that red mulberry, causinig hybrid mulberries to form. Because white mulberry is so much more abundant, red mulberry's genes may eventually disappear. White mulberry fruits are edible but not nearly as flavorful as red. Chinese use white mulberry leaves for sheep and cattle fodder."

Also, be aware that the berries of white mulberry, M.alba, are not necessarily white - yes, there are some white-fruited selections(in my experience, they're lacking in flavor - just sort of sweet and 'grassy'), but the vast majority produce lavendar/purple berries that can stain - whether tracked in on the bottom of your shoe, or in bird poop - as surely as any good M.rubra or the rubraXalba hybrids like Illinois Everbearing.
IE gets my vote as the best-tasting mulberry I can grow here, but the trees eventually become huge! I've not grown Geraldi, but have friends who have, and they like the fruit, so if you must have a small one, I suppose it would get my nod.

Thanks for all the advice. I guess I need to think it over a bit more.

I never eat Mulberry fruit before. However I remember when i was a child, my mom boil the mulberry (silk worm type) leaves and made kind of 'tea'. It tastes quite good and helped to deal with the hot weather (100 F).

I did some research and the silk worm mulberry is the white one, Morus Alba type. I looked up on Raintree nursery and saw couple of them.

I just wornder if anybody has used the leave of white mulberry to make tea? I like the Illinoise everbearing, but that is hybrid, not sure I could use the hybrid leave to make tea.

Any info would appreciate.
Thanks
Alpharetta