Canon's and Nikon's are typically known to be the best...as far as image quality goes. SONY however, can also be good for some things though too. Depends what your end-result picture goal is.
I have a Canon high-end SLR camera (EOS-40D)....wish I would have gotten the slightly lower end Canon Rebel SLR now (think its more my speed, for now anyway). It takes excellent photos, however you need to know how to tweak all the bells and whistles, utilize the lense to realistically get the GREAT shot. The Canon Rebel SLR does much the same, but would have been less high maintenance.
Last year, decided to get a mid-range camera...for many of the same reasons you mentioned (to get the easy, quick shot, ease in portability, etc). And got the Canon Powershot S5IS (8.0 mega pixels). Mostly got it as it is mid-size (smaller than my SLR) and heard it can take both pictures and good quality video. However, quickly learned that although it can take movies...I'd have to first convert the .AVI video format to a .MOV file format in order to be burned to a DVD for viewing on the TV). Its sort of nice...but way TOO many times it MISSES the shots! I got it to actually replace my SONY Cyber-shot (that had 3.3 mega pixels)...but to be honest, my old SONY got the shot 100% more times than this supposedly better pixeled camera. Also invested in a Nikon Cool Pix for my purse (instead of the phone camera). They're tiny and easily shoved into a small purse and comes with a nice sleek-lined carrying case as well). It does a great job on pictures (for those times when you need to get something in a pinch).
A friend of mine recently got a Canon PowerShot SD1100 IS, Digital ELPH. 8.0 mega pixels (from Target). She wanted something simple to use but with good pictures too as she is not very savvy at all to the digital world yet. Hers is a fairly sleek, slim-lined model...so also could easily fit into a purse or small bag. And I have to say the shots she has gotten with this are FABULOUS! ...and it seems she always gets the shot without much over-exposure or under-exposure to contend with. She took shots at my son's birthday party the other week...and they all turned out really great (at a bowling alley...where it was dark, and also cosmic lighting was going on...definitely a tough place to get good shots!). Neither of my two higher end cameras were getting the shots like she did so effortlessly. So, actually am hoping to now get rid of my Canon PowerShot and trade up for the one she has now!
Also it might not hurt to check out a 'National Camera Store'. Maybe a couple trips...to get a couple different sales people's perspectives. They are VERY knowledgeable there. People that work there are people that live and breathe this stuff. And for their job there, they play with the cameras there all day long. And can tell you more detail of what they can do for you. They'll even allow you to test the cameras there...to do some picture taking on your own. Think you also have 30 days to play with the camera and return it if you don't like it (double-check on how that policy all works though...before purchasing). Also, bench mark their prices against other places (Best Buy, Target, etc...) as you will want to make sure to get the best price at the end of the day (think they price match??). Another thing that's nice about National Camera...is that if you buy a camera with them, you get a FREE camera class. Helps with the learning curve...as they'll teach you how to use all the features (bells and whistles) on your new camera...to get the best shot you can.
Best of Luck! Hope something here helps! :)
R~