Here's my process for caring for a hide starting with the skinning process. When I skin, I take care to not have large chunks of muscle attached to the skin. It only takes a little longer to do this, and it's easier to do when skinning than it is to do later with the hide flopping around on the ground. Next, if I'm in the field and don't have salt, I'll either hang it so that it can drain, or, if I'm transporting it back to the truck, I simply let it drain for as long as I can (usually while quartering or deboning the animal) and then roll it up to be packed out.
I don't flesh the hide prior to salting - I flesh after salting. Once I get it to salt, I apply a liberal amount on it (about 1/4" thick), then I fold the hide (not roll, but fold) and set it on a piece of plywood at about a 45° angle so that it will drain (a folded hide drains well, as long as the open end is facing down). Every day or two, I brush off the old salt and put fresh salt on it. After 3 or 4 days, I brush all the salt off, and then it's either off to the fleshing board before I start the tanning process, or I stick it in a big zip lock bag and put it in the freezer until I'm ready to tan. The hide will keep in the freezer almost indefinitely.
If you're wondering where to find non-iodized salt in large amounts (50# or more), just go to your local livestock feed store and ask for "mixing salt". It's used as an additive for feed and available in large amounts for decent prices.
Hope that helps!
Scott