I had 26 VA's last month and now I cut it down to 15 with the same work done. So I think Im qualified to answer your questions.
Ideally it'd be a managed solution (tiered with an assistant working through a management structure that checks their work, or distributes work through a team), but I'm not sure that that's possible
Yes its possible. Distribute the resources, like a puzzle, never give ALL 1 process to a VA unless you know him/her personally. With my experience, giving a whole loads of info on your VA just makes them
1. In over their heads, demanding more salary every 2-3 months.
2. Stealing your process and making them a competitor in the long run.
Here's my tip in work distribution. For example this is a service like mine, I have FB, Twitter, Pinterest, linkedin and more. 1 VA will handle account creation on FB, pinterest and 2 more. Another VA will handle the Pinterst, Linkedin etc creation. 1 VA will manage the posting on FB, 1 VA will manage the follows on INstagram, pinterest and twitter. So 1 small process is divided into chunks. On the other side it can never be complete unless all ot them finishes their work, and for example 1 VA did not finish the work. You are there to get it done.
What kinds of pay structures exist (hourly/salaried/per piece of work)? What kind of rates am I looking at? What kinds of work should I completely avoid giving the VA?
Depending on the work done. My service is a monthly contract with clients. and MY VA's are getting different salaries. Like the account creator is on Commision basis, per piece of work. But my Follower guy is on a monthly basis NOT hourly. Getting in on hourly rates will just cost you morei n the long run. Have a contract ready on a monthly basis cause its much more cheaper and you will not have to give out money every single day. Ofcourse if you are starting out a daily rate in 1 week is required but after that every 2 weeks would be nice for both parties.
"Any other tips? Any other resources on VAs?"
Most of my VA's are from the Philippines. I got 2 from Odesk, 4 from freelancer dot com and mostly are referrals of them. Yeah they have problems, but hey they're the nicest VA's Ive ever met with an average SEO knowledge, great to talk with and are always following good instructions. Problems with My Va's are minimal like storms and floods and that's about it, but is a big hit cause it takes them almost 3-4 days.
Absents are minimal(aside from the storms) cause I give them Attendance Bonuses. I call them everyday from skype to check how they feel (cause that's more important to me than anything) How they feel = Results on my work. So I always encourage them to feel good and always to smile cause it reflects in their projects. Anyways feel free to ask more if you need more answers.