Selecting a sweep (curvature) is easy to do from the London Pattern Book (aka Sheffield List). For this radius, I'll guess more than a 7 and likely a 9.
The #11 is a distinct U shape so you could work with a narrow one and work around to make a bunch of cuts. Hide the tool marks with sanding.
Good gouges are costly but you get what you pay for. Pfeil, Stubai, Henry Taylor, Ashley Iles, possibly Narex and Arioux are the best.
Fortunately, you don't need one of everything to begin with. I buy one at a time from open stock (Pfeil), maybe $300 to set up 15+ years ago,
then one or two every year since. I needed other gouges to do different things as my carvings went from 8-10" up to now 64" tall or like a turtle 18" x 16" x 4" for the shell/body.
Should you wish to use the excellent wood carving tools common here in the Pacific Northwest, adze blades alone will set you back $50 - $100 each and more.
Crooked knife blades, even good farrier's knives to be rebevelled, run approx $50 a piece.
Maybe 30 gouges, a couple of adzes, 15 or so crooked knives = looks like a lot but they were a long time in coming.
I could do those pits with the crooked knife (yellow whipping) by spinning it around. In a past life, it was a farrier's knife for trimming the tow nails of sheep and goats..
The curved piece of birch will become a bowdrill in a fire set, a pair of carved Ravens to hold the cord on their beaks.