that second shot, check the minimum focus distance on the lens, are you too close?
suggest you brush up on your skills before spending lots of money, the 300 will give good results when operated right, a more expensive camera (with more control permutations) could just give you more problems!
I'm with Janice on using cetre focus point only, gives you lots more control, certainly until you have a better understanding. I've got the 400d and you have to be in one of P, Av, Tv or M modes to allow focus point selection. The green square (full auto) and all the preset icon modes dont allow focus point control.
If you can get it into centre only focus point then in one-shot focus mode (not any of the AI modes) then you can half press on the shutter, it locks the focus on the centre point, then you can swing the camera around a bit to move your subject away from the centre and it will hold the focus until you release the shutter or press fully to take the shot. Obviously dont move towards or away from the subject while shutter is half pressed as you'll muck up the focus by changing the distance. Note when doing this that if the distance to teh subject is short then the depth of field is very narrow too, possibly a few mm and any small movement by you towards or away can ruin the focus.
I'm no expert, it's just that I just get it wrong lots and now I'm starting to realise lots of reasons why!
I just got a 50mmf1.8 and my first shots were not stunning, trying it on f1.8 I was getting very narrow depth of field, inside the house and in the garden at short range it was a bit of a disaster, especially with the half press to focus and recompose routine, it was getting out of focus on my body sway. But then we went out & about for a play and I realised it's sharpest at f2.5-f8 where it also gets a bigger depth of field, and helped also by subject distances over 10ft (and with decent shutter speed to account for my wobbling) and then the results were very sharp.