Cheddar - stick with it and you'll get there!
Here is what I see from your two shots:
#1 - lots of noise. I'm guessing this photo was way darker before you put it up? With a shutter of 1/800 and f8 you've got almost no light coming in to the camera.
Use 1/800 and such when you want a black background and have a light sourse (your internal flash or an external strobe) to light your subject.
F8 is great for those really close up macro shots. Otherwise it will often just be too smal to let in enough light for a good exposure.
Taking a guess at your conditions, I'd set up in M mode with 1/100 and f4.5 or f 5.6 if it was really bright. That should get you in the ballpark. Background water all wishy washy with those settings? Head for 1/125 to darken it, give it more oomph. I wouldn't drop below 1/100 or maybe just maybe 1/80 in a pinch - you might find you get camera shake with speeds less than that (1/60).
#2 - 1/60 was too slow. You have too much light here and it's all washed out. Personally I'd rather see it a tad darker, even at the risk of maybe losing a bit of detail. You're also a bit far away so any internal flash you had wasn't reaching your subject. Try a bit faster next time to see a bit less blown out bits. The ISO 100 is what I leave my rigs on almost all the time unless i really really need more light.
5.6 should be a good starting place for your aperture combined with a faster shutter. 5.6 should give you pretty crisp images on a variety of subjects; you might even try f6.3 or f7 if you've got a ton of light coming in.
I don't like opening the aperture up much beyond f4 - any wider and the images often look pretty soft. Most compacts don't do as well at their maximum apertures - usually around f2.8 or f3.something - so setting it slightly away from the maximum helps your lens work near its "sweet spot"
I know you'll get there! Keep shooting
