Small project studio assistance.

Hello DP community!
I need assistance with setting up a small home studio. I am trying to create a set up that's relatively portable since I do family portraits (approximately 4-6 people) both indoors and outdoors (my house and at my relatives house). I will very very rarely shoot full body portraits.

I would like to know:
- What speedlights I should use, since I feel like I outgrew my single 580ex ii. I was considering the Yongnuo 560ii or the Yongnuo 565 (since it has HSS). I will also consider another 580ex ii or 430ex ii.
- I would like to get both softboxes and umbrellas (since I realize that they can serve different purposes). What is the optimal size for both umbrellas (i'm considering 43") and softboxs (28" square softbox or 24" x 36" / 32" x 48" rectangular)?
- Whether I should use the optical trigger on my Canon 60D or purchase radio triggers such as the Yongnuo yn-622c?
-Are there any alternatives to using HSS if I shoot outside (such as using an ND filter), or should I purchase a speedlight that has HSS capabilities?
-Best cases or bags to store speedlights, stands, etc.
-Best material for the backdrop (Would prefer to go the DIY route since I have a relative who is a tailor, who can acquire the materials for me rather inexpensively).

Please do not suggest strobes since I currently do not have the space or ability to travel with those at the moment.

I appreciate the assistance. The community has been nothing short of helpful.

--
"In the Internet age, the bathroom is now the photography studio.In the film age, the bathroom was the developing lab.
And before the film age, I guess it was just the outhouse." - Anonymous