I always spray on the batting but I don't think it really matters. When I first started using spray baste I would often overspray and had less issues with that going into the batting. Before I use my batting though I fluff it up in the dryer to get out any creases and such.
I don't have a lot of room in my house and much prefer to use my friend's long arm! But when I can't the long arm I use my queen bed, first I take off all the blankets and pillows (so usually combine this with fresh sheets/laundry day). I have rolls of brown heavy kraft paper, like the old fashioned paper bags (not the new thin ones). I cover my bed completely with those. They are waste product from hubby's work. Before I had access to them I used vinyl tablecloths I got from Big Lots/Dollar Store, or the really flimsy plastic ones for birthdays or holidays -- pick them up after the holiday when they go on sale.
Typically I put the backing on first, so the fluffed up batting is laid out and then the back (or top) is folded in half. and positioned over the batting. I find I can only be good about 1-2 feet at a time, the first set is very important because once it is on I can reposition the bundle towards the foot of the bed where I can go a full row at a time. So that first set I spray from about halfway on one side then go to the other side. Then I lift up the fabric and smooth it down over the sprayed part, repeating on each side of the bed. Then I can slide it down closer to the foot of the bed and go across, still only 1-2 feet at a time.
Then I make sure the back is on nicely and firmly with no wrinkles and flip the whole thing over and start again with the top.
Before my husband moved in (16 years ago) I had enough room that I could move the furniture in the living room and would lay the quilt out on the floor using canned goods to hold the backing fabric down. Now we have all sorts of habitats with snakes and lizards and such in them... My bed technique may be physical and awkward but still better for me than crawling on the floor!
My friend Pam uses the board technique. She happened to have a couple nice pieces of trim left from a project so they aren't as thick and heavy as 2x4s but are still stable. She staples the fabric to the wood and winds it around, and then attaches the other end to the other board. Then she can position her fabric snug with a 2-3 foot opening that she works well in.