The Powershots are a great camera so if you're "upgrading", a SLR is really the only thing to get. You could get another compact but it wouldn't be vastly different to what you've got (you could get one with a bigger zoom and an image stabiliser say, but you'll still have the other limitations).
But keep your compact and take it with you. In my opinion, a compact camera is worth just as much as an additional lens for your SLR.
If you're going the SLR route, a Canon SLR will be laid out very similar to your Powershot so the transition will be easy, but Nikons are great too. I wouldn't buy an expensive camera body - something like a 450D would be very good. Spending more on the camera body won't net you much difference for your purposes, you're far better off spending the money on lenses.
To help with flare, you can use your hand or a hat or anything handy to shield the lens from the sun (or a lens shade, obviously). If the sun is behind you you'll be fine, but if the sun is in front of you even a little bit and the sun's rays are shining into the lens you'll risk flares. You don't have to hold your hand right next to the lens when you shade it, as long as the sun's rays are not shining into the lens.
A general rule of thumb in photography is to put the sun behind you (but not directly behind, because your subject won't have any visible shadows and your picture will look flat). Generally, the more into the sun you shoot, the more colour you'll lose. If the sun is in front of you a little it won't make too much difference, but any more and it can affect the shot considerably.
Spur-of-the-moment photography is damn hard. An SLR will make it easier - they have manual focus but also their auto focus can work on a specific point. Compacts are hard because you can never be certain exactly what they're going to choose to focus on. SLR's are also generally faster at focussing (depending on the lens) and take the picture quicker after you press the button. A fast motor drive (ability to snap many successive pics when you keep your finger down) can increase the chance of getting "that moment".
Low light is something that will always be a challenge. Even with a very fast lens (one that can open very wide and let in a lot of light), you'll still reach points now and then where you come unstuck. If you can avoid a flash do so, because it robs colour and shadow detail. Steady your hands or arms on any object you can. And watch the shutter speed. Compacts often choose a stupidly low shutter speed. If you're shooting at 1/60th of a second, you have to take care not to move. Anything slower (such as 1/30) and you're going to have a really hard time keeping steady.
As a general rule, tuck your elbows into your sides for more stability during normal photo taking.
Perhaps one of the best and easiest tips for getting colours more vibrant is to change the white balance on your camera. Auto white balance tends to produce quite blue shots, which makes them look washed out.
The white balance presets of 'daylight', 'shade' and 'cloudy' white balances are warmer (cloudy being the warmest (most red) if I remember correctly). I would use 'daylight' for pretty much everything outdoors. Your pictures will have a nice warm tone. You can even use 'shade' for all outdoors pictures, it'll be warmer. Be a little selective with cloudy - it's really quite warm and could outdoor shots in bright sunlight a little too red. But I'd use 'cloudy' for pretty much all shots in the shade, or if the day is in fact, cloudy. Basically, the less light you have, the less colour you'll have, and the warmer the white balance should be. Hence the names of the presets.
Indoors you can use the daylight setting, but it'll often be too warm. I'd drop back to the 'fluorescent' setting which is a little cooler than 'daylight', but still quite warm. You'll also have 'tungsten' available, but this is a very cool setting for use under light globes. You might still find it too cool for your tastes so you may want to use the 'tungsten' present even under light globes. I'd use the 'daylight' setting at a concert without much worry, or you could drop back to 'fluorescent''.
If you get a SLR, a polarising filter will help you get quite a lot more colour (if need be, you can also shoot through polarised sunglasses on your compact or SLR, you'll get a similar result). You'd be amazed at how much light reflecting off some objects obscures their colour. Foliage is a prime example - it looks far more colourful through a polarising filter.
I hope that's useful, sorry if I went over stuff you already knew.