You need to make sure it's 100% dry. That is actually the hardest part as it always seems like there's more and more water that comes out. Worse is near shower pipes. I don't know what it is with showers, but they always seem to have an unlimited amount of water left in the line. You may need to open a faucet at the highest spot in your house and one at the lowest to drain all the pipes. If your water heater has a shut off, does not hurt to close it off either. Before you start, close all the faucets that you opened. The pipe in your picture may be a little tricky because there will probably be water that wants to come down. Though before you cut you can always open those two valves and let it drain as much as possible.
Shove paper towels up the pipe until they come out completely dry. If it never happens you may need to go the bread route.
I try to solder all around but you don't really have to as it gets sucked in. I like to try to get visible solder all around as it gives it that professional look. Wipe off the flux after it cooled down. Do not turn on water till it's cool enough to touch, you don't want to "shock" it.
If you are adding anything new, it does not hurt to put a valve first. If I was to redo all my home's plumbing I would actually have everything going to a manifold with valves. It's nice to be able to individually shut off water to specific areas.