I know it's a little tangential, but I recently stumbled onto an alternate configuration: Set it to always show, minimum icon size with maximum magnification. It still takes up a little bit of screen space, but I can get to it instantly, and so far I have fewer accidental activations because the small icons take up less surface area on the edge.
For the vast majority of properly-designed Macintosh applications, deploying to the /Applications folder is not necessary.
However, it is considered a best practice. When someone is working on your Mac (EG, one of the employees at the Apple Genius Bar), having your applications located in a single, sane, system-recognized place makes life considerably easier for them. It's also plausible that a poorly-designed app may misbehave when not installed to /Applications, although I've not typically found that to be the case. Some newer apps are detecting when they're launched from somewhere other than /Applications (typically the .DMG from their download) and automatically installing themselves correctly.
If you want to quickly access an application which is deployed in the /Applications folder (or you simply don't want to dig through a zillion entries to find the app you want), I recommend using Aliases (Command-L in Finder), and placing the Alias wherever you like. For example, I use Dock folders ("Stacks") full of Aliases for all my app-launching needs, with folders for Development, Productivity, Multimedia, Games, Internet, etc.
Whenever someone asks a question such as this (or, alternatively in the Windows world, "do I need to use the 'My Documents' folder for my files"), I always ask back: Do you have a genuine, critical need not to do so? One which isn't addressed by the in-box aliasing ("shortcut" in Windows) mechanism?
Best Answer
Double click safari to open it. Then, when it's open, right click on it's icon on the dock (which you call the system tray), and say `keep in dock' (or options -> keep in dock on snow leopard).