An update on my experience: it still seemed as if the "Automatic (push)" delivery of my Yahoo mail was inconsistent, and setting it up as a generic email account (as opposed to selecting "Yahoo" from the preset options) only gives you the option of pulling new mail in every 15 minutes.
So now I'm trying the K-9 mail app. The good thing about this app for me is that it lets you pull in new email in smaller time increments if you want - 1 minute, 5 minutes, 10 minutes, etc. And that seems to work fine, so that's a plus. Unfortunately, the mail "push" feature - ie, mail comes to your phone right away whenever your email account receives it - doesn't seem to work with Yahoo either, just like the stock email client.
I'm more satisfied with K-9 so far than I am with stock because of the fact that you can have it pull mail in more frequently (and it also has a number of nice features such as letting you change the color of the notification light), but I still think it's lame that "push" doesn't work. I read that an application called MailDroid does have a "push" feature that works with Yahoo, so I may try that. It's ad-supported though (or $18 to buy). And there's also a Yahoo Mail app (ad-supported) that I might try.