Looking for a new self-propelled mower for hopefully less than $300.
I'll be mostly bagging on a flat lot less than 1/4 acre with lots of
turns around shrubs and trees. While performance is important,
reliability is the most important consideration. Not being
mechanically inclined, I need to know that whatever I get can do the
job it's supposed to do without a lot of messing around or running to
the repair shop with it, warranty or not.

Any suggestions for reliable mowers in that price range?

I can suggest some features, but not brands:
* Big rear wheels make moving over stairs and through boggy spots
easier.
* Swivelling front wheels make turns easy. You don't have to lift the
front of the mower to turn.
* Engines with iron piston sleeves last longer.

The others' suggestions are good:
* Consider mulching instead of bagging. Mulching is only a problem if
you over-fertilize in a desert area (where grass clippings don't rot
quickly).
* Go to a local repair shop and check the used mowers. They'll sell
you a high-end mower for a low-end price. They'll also tell you which
models are the most reliable.

--
Steve Bell
New Life Home Improvement
Arlington, TX USA