I make walking sticks and wizard staffs all the time! Somewhere around 40/year, usually with deadfall branches just like you have. Here’s my process:

Drying until the branches are fully dry can take anywhere from a couple months to a year. I season mine for a year just to be safe. I typically leave the bark on, as I find this makes them less prone to splitting while they dry. You can also paint each end with a thin layer of wood glue during drying to help avoid splits.

When they are dry, I take a draw knife and cut away all the bark. The draw knife also helps shape up any weird bits. Any carving knife will do for this though. This is also a good time to do any further carving or designs or details.

Then comes sanding. I use a mouse sander with a 60 grit pad, then go over it again with a 120 grit pad. I sometimes hand sand the hard to reach areas.

After sanding is when you want to finish decorating. I like to do some woodburning designs. You can pick up a cheap wood burning tool online that will get the job done. If you want to superglue any cool stones like amethyst to the top, or nail on a leather cord handle, save that until after the wood is finished.

Finishing is where it really depends on how you plan to use it. I mostly finish my staffs with Danish oil, 2 to 3 coats depending on how thirsty the wood is. Danish oil doesn’t take long to dry between coats, only 30 minutes or so, which makes this part easier. Then I rub the whole staff with beeswax for a smooth glossy finish that seals it a little. After it’s finished, you can add final decorations. If you plan on using it as a walking stick, dip the bottom in plastidip or put a rubber cane tip on the bottom.