Thanks for the replies and suggestions so far! This is not an heirloom piece of furniture, so I'm not too worried about getting it perfect, because I don't want this to turn into an involved project. Based on what I've learned so far, I think I'll give the Danish Oil a try, because the idea of applying it with a cloth appeals to me. (I'm not great with brushes and spray cans.) Shellac, from what I've gathered, is very involved and seems more suited to high-end applications like fine guitars, so I don't think I'll go that route. My reservation against poly urethane is that it tends to give an amber hue to the wood over time, which I'd like to avoid. Also, the PU coating that I've applied to my hiking sticks in the past all have maintained a slight "rubbery" feel, which is great for the hiking stick application, but not appealing for a piece of furniture that I'll be sitting on.
If I can believe this article, I think Danish Oil is the way to go for my project:
https://www.instructables.com/id/Applying-Danish-Oil/