Thanks very much for all the responses.
At this point, to get my old 2-cycle Lawn-Boy working I would need a new gas tank and a new carb. Also, the spark plug will no longer tighten. I'm not sure how that happened, but something felt funny when I removed the plug to clean it, and now it won't tighten. I don't know how I could have stripped it while removing it, but I guess I did.
So, I think to fix all that would cost more than a new mower, and you know, it is 30 years old. I think it's time to retire it.
I've got one area that's very close to my pool, and I've learned the hard way that things just work better if I bag in that area. It's actually less trouble doing that than dealing with all the unbagged stuff the wind blows into the pool. So that's why I need a bagger.
Well, based on the comments I think I should look at Toro's, and perhaps look at what Sears and WM have to offer, just in case. I would expect Hondas to be wonderful, but keep hearing the opposite from a number of people here locally.
And I'm gonna stick with a push mower. Self-propelled is just something else that'll break. I don't know if they make 2-cycles anymore (Sears maybe?) but I would certainly look at one of those.