I created an account JUST so I could answer this for you as I know the answer and it is nice to have one posted. I was actually looking up a different problem with mavericks mouse when i saw this one.
SOLUTION:
reason you are having to click on the mouse in system preferences to activate the drivers is because the MicrosoftMouseHelper.app is not auto-launching. This is probably due to the driver not updated yet. All you need to do is go into your sys prefs > users > login items and add the app mentioned above at this location (just use the go-to-folder in finder).
/Library/PreferencePanes/Microsoft Mouse.prefPane/Contents/Resources/MicrosoftMouseHelper.app
As for your hesitancy to upgrade, I just went from Snow Leopard to Mavericks and so far there are only small pitfalls. If you are in ML, I am betting it is only an upgrade as i keep reading that "this is fixed in mavericks."
The mouse issue I am having is a big pain though. It has only happened twice so far, and it means I have to at least log out to fix it. The mouse disappears. The cursor i mean. The physical mouse still is active, buttons work, but there is NO POINTER anywhere. It seems to happen when i hit my expose corner, err my bad, mission control to show all apps, then it disappears. As for suggestions, I did not do an upgrade, i did a full clean install. My computer is a macbook pro 17" early 2011.
Oh and finally, you DO NOT want to use usb overdrive. The reason why the microsoft mouse stands above the rest for mac, is because it has the microsoft acceleration built into the drivers. What this means is how far it travels based on how far you move the mouse and and what speed you did it at. This is the ONE thing I have always praised microsoft over mac, was mac's acceleration never felt natural compared to a windows machine. (keep in mind I have not used a native acceleration in a LONG time so maybe it is better now in recent OS updates)