Lots of thoughts. For one, get on YouTube and look up Spoon Club and "Barn the Spoon". Both will show you wonders ;)
I find holding the piece in my hand much easier than trying to work on a piece held by a clamp, when I'm spoon carving. You need to shift around and account for different grain constantly, making holding it in my hand infinitely more practical. The slojd style knife with a flat scandinavian grind, like the Mora 106, is made for carving the outsides of spoons - everything but the interior of the bowl. The hook knife does that part and better than any other tool. With a gouge, you Must clamp the work, not hand hold it. With the hook knife it's easy to hand hold the work and so adjust angles and get around the bowl in a smooth fashion. With really sharp knives, you get a finish from the tools that does not need sanding.
Here's the first in a series of videos that explain and demonstrate the knife techniques used for carving wooden spoons using knives, the carver is Jogge Sundquist and he knows his craft, he's been at it all his life ;) https://youtu.be/3J6OMWUfzD4?list=PLoaPpRkFfg5WkjHrJZ02ooSH16nV2-TBU
A shaving horse is a fantastic tool to have for all sorts of green woodworking (or just woodworking, period) purposes, but for spoon carving, if you need something to hold the piece other than your hand, the spoon mule is the right tool for the job ;)
Absolutely true that the bowl of a spoon is nowhere near so deep as we think it is ;)
Many wooden spoons have incredible amounts of "crank" - that's the angle between the handle and the bowl. Cooking spoons tend to have little or none, while "eaters" can get very extreme.
There's an interesting tradeoff that happens at the "neck" of a spoon, where the handle flows into the bowl. For comfort in your hand, the neck wants to be narrow, but with wooden spoons, a narrow neck will often mean a broken spoon if there isn't something to compensate for getting so narrow. This is why at that point many wooden spoons become deeper - the handle has been broad and flat, the neck becomes narrow, but deep and the keel formed there will often flow into the bottom of the bowl of the spoon. The result is a spoon that is both comfortable and sturdy.