Is it me, or my 450D? Focussing and image quality

I think it's really possible to over-think this.

Forget about choosing individual focus points other than just selecting the center one, which is the most accurate (cross-type) anyhow. With your kids moving around there is no way to know which focus point(s) would be relevant.

And IMO AI-Servo can be more trouble than it is worth. Unless your kids are running around towards and away from you and their actual focus distance is changing, servo is likely to just get confused and you'll snap a shot while the lens is hunting for what it hopes might be the thing you're trying to focus on.

I have the best luck overall using the center focus point, one-shot AF, getting the center point on the subject, doing a half-press to focus and then holding it there til I decide 'now!' to press the shutter. If the subject moves much I can easily repeat the process and get a fresh focus.

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Do people really spend $700 on a camera so they can take a picture of a squirrel or a duck?