Yes, get thee some kind of stand so you have a way of getting your bike off the ground without having to turn it upside down. You don't want Simple Green getting into the bottom bracket and other places on your bike as it really is a de-greaser. It will strip every ounce of good grease off and then you'll be in serious trouble!!!

I have, on occasion, used Simple Green in my chain cleaner as it really gets the chain clean. However, you MUST oil your chain after you get it completely rinsed off. Let it sit awhile to soak in and then take off the excess.

I see by the specs that you have a ten speed. I have a ten speed bike as well and have found that the chain wears out much faster than my nine speed. (this may change as I have upgraded from an Ultegra chain to a Dura Ace chain). If I were you, I'd get it check for stretching every 1000 miles or so. The other component that I find needs adjusting is my front derailleur. It's a tricky adjustment so just listen for noises when you are shifting. Often you can adjust it yourself by a 1/2 click on your left lever (the one that moves the chain in the front).

Looks like you have a nice bike for your needs.