On Sunday I picked up more photographic stuff at another car boot sale (US="swap meet" I think), one of which was one of these, which I initially thought looked interesting but got a bit dubious about, especially when I found out that the photo conversion software is hideously expensive. But when I checked it turned out that CEX (a big UK chain of 2nd hand electronics etc. stores) will buy them, and for about £16 more than I paid for it if you take part exchange rather than cash. They also offered an Eos 500D at one of the local branches at a price I could afford, especially with that thrown in for part exchange... Cue visit to local CEX store, and purchase of the body (with three batteries and a charger) for a bit over £100.

I went to the park and took some test pictures today using my 18-55 zoom, unfortunately not in very nice conditions, it was very overcast, and was a little disappointed; they don't feel notably better than I was getting with the 300D, and in general were not particularly sharp. But the metadata shows that they were all fairly low speed and wide aperture, which does tend to have that effect. I've since tried with the 50mm lens I got, and in program mode rather than full auto mode, and got much better results, especially with flash. I'm not going to post anything today because they're much better pictures of e.g. the mass of computer cables hanging on hooks on my work-room door, random books, etc.

My feeling at the moment is that it's working, but I really need to up my game on selecting appropriate camera settings, it's less forgiving than the 300D or my old Nikon. I suspect that I also need a better lens, the 18-55 isn't wonderful. I really hope that the weather's better tomorrow, and I can get out and give it another try.

Yup there a plenty of factors to consider.
If you apply the inverse rule to account for freezing camera shake (1/focal length) you will usually be in good shape for eliminating that as a culprit. So if you were at 1/50 of a sec the shutter speed shouldn't really be a factor for those lenses.
You are correct wide open can be a bit soft depending on the lens so if you stop down that will improve. Primes will have better optical performance than the comparable zooms in their range. (I.E. Don't compare a cheap prime to an expensive zoom) Either way even using the lower priced lenses you should be able to get good results with some attention to the limitations of the lens, and a maybe a little sharpening in post.

Another factor to consider since you mentioned shooting in auto is that those auto modes that produce JPGs will process the photos in camera which will apply settings to color contrast, etc including sharpening, whereas the raw file wont have any of that as it expects the user to apply the settings in post production to their specific taste/need.
Also stepping up to a 15MP over a 6Mp and adding 2.5 to 3 times the resolution may be part of the reason you feel like the camera is less forgiving.

I've returned it - the results I was getting were poorer than I was getting with my Eos 300D using the same lenses etc. and the same magnification, and I really don't want to spend weeks trying to tweak it. I think something was slightly out of alignment, just enough to put it slightly out of focus, and I just don't trust the camera. I'd sooner start again with another body, and this time take a laptop to the shop so that I can see the results of a couple of test photos before I take it away.