The home button doesn't kill apps and should just bring up your Sense UI middle/main screen.The back button behavior is controlled by the writer of the app in question. For instance I have a solitaire game that uses the back button to undo moves, rather I had the game it's un-installed now because of that very thing, and you couldn't "back" out of the game at all. The browser uses the back button for, well, back and doesn't back out. However I have been reading some of the in-depth threads over at xda developers and have come to the conclusion based on the evidence there and the performance on my hero that most of the time you don't need to kill applications at all.
I came from BB -> Sprint Mogul -> Touch Pro -> Hero and even though I work with Linux for a living and know Android is Linux I will still searching for a good task manager. The honest truth about task managers on Android is that you only need them to kill misbehaving applications. The Linux scheduler that Android uses is quite good at taking care of memory use and the CPU is not used unless an application is active. Most of the folks wondering about memory usage don't understand how Linux works on that front. Linux will use every bit of available memory it can all the time and release what's not actively in use, like for a sleeping app, as needed. So unless an app has a memory leak then it's not actually tieing up an memory and unless it has sleep issues then it's not tieing up the CPU. When I started looking at things for the right perspective, read: this is linux not just another smart phone, then I realized that a task "manager" isn't necessary just something lightweight, that exits or sleeps when I push the back button, that will kill an out of control app is all that is necessary.
All that said there are plenty of apps that suck at both sleep and memory leaks and it can become necessary to kill them. So far, and based on my professional experience with Linux, Taskiller is the best app for most users as it only shows applications and doesn't let you screw up your phone by killing processes. It does one thing and does it will. If you are lazy you can set up the ignore list, on the paid version which is cheap, and then use the widget to kill everything else. What I use it for is to kill off the occasional ill coded app right before I uninstall it. With the exception of the sleep issues with the messaging app I can have everything stock running and have no performance issues even an extraordinary number of widgets.
So the answer to what you want to do is, technically, that it's not necessary. I know that's probably not the answer you want but the rest of the answer might suck even more and that is that the behavior you want is controlled by whoever wrote the app and not the OS. If you want to kill apps, which can in some cases screw up the app and cause a re-install, you'll need a task manager. I would recommend not killing apps outright but rather figuring out which apps are screwing up your performance and find a replacement for them or kill them when necessary, one at a time, using the free version of TasKiller.
