Casperc - I'd tend to go with those advising to do a colour image initially.
Firstly - doing that, you "do have" the colour version if family or friends want that instead. Also, kids who want copies to take to school, or for collections, often aren't much into appreciating the art-value of B&W, and prefer the "brighter" colour versions.
Where I'm coming from is having an SX10 for over 2 years - which does very good Superfine JPEGs, then having a Fuji HS10 about 8 months - which has the RAW and RAW+JPEG options - but one doesn't always have RAW selected when something happens...
After initial experiments "to see what the camera itself does", I haven't used the B&W in-camera functions. With JPEGs, which have limited data content anyway, you can do very little later to what minimal data is left in a camera B&W conversion.
Even as JPEG, the colour image does have a lot more information in it. The camera B&W is a 1-channel greyscale image only. Very little "info left in it". But if you have the colour image, you have the RGB channels, and even if very limited compared with RAW, the 3 channels have more depth and dynamic range than a single greyscale image.
To do anything other than very mild 'tweaks' to JPEGs, as that's a very "lossy" format, convert the JPEG to a "non-lossy" format. With Photoshop, PSD - Gimp, XCF, and TIFF will work in either. (A TIFF converted JPEG handles much as a TIFF output from RAW processing, except of course has less information in it to use.)
I'll assume you're using Photoshop, but Gimp and others have similar functions. Open the TIFF (or PSD) in Photoshop. Then open the Channel Mixer dialog. At the bottom of that is a checkbox 'Monochrome' - so select that, and 'Output' in the top field will change to 'Gray'.
You then have the RGB sliders still active - and an adjustable 'Constant' slider below them. Leave that centred until you have the best result selectable from the RGB sliders. If not then as desired, try altering the Constant in small increments and use RGB sliders again.
Using the RGB sliders, you'll find that you can bring out more detail in shadows, and also have a more accurate range of "shades of gray", contrasts, and depth, than the camera's "greyscale conversion" - what it's actually doing is little better than a processor-preset "desaturate" function.
As P&S, however good, sensors tend to be noisy, you can with the RGB sliders, watch the darker regions of the image - and those that are close to being "1 shade", such as sky or flat water - and adjust for visible noise. Use small adjustments on the Constant bar to lessen noise, while keeping the other ranges of shades as you want them.
When you have the result desired, click OK and close the dialog. You can then fine-tune with the 'Levels' dialog. If you think you need to Sharpen - use USM - but only with small amounts and a narrow radius. Be gentle on it - there's less information in the mono image, so small amounts will have a 'harder' effect.
Obviously, you can do all of that, and better, as you'll have more info in the output TIFF, with processed RAW files - but you can of course do more in the RAW processing, too.... This is just what you "can" do with good JPEGs - if you forget to select RAW - or didn't have time to without losing the image-instant.
Or, if, like my SX10 - the camera doesn't natively do RAW, anyway...
Dave.