Out of that list, I'd say networking is the most important because every IMer has to do this. Traffic and list building are important too, but not every IMer has to do these things.
I would disagree with your #1 and #2, Obadiah. I'm actually not even sure what you mean by "payment processing"...do you mean one should familiarize themself with Clickbank and Paypal? Because it's not necessary, and even if you wanted to, it would only take a few minutes each to orient yourself inside.
Web design is a totally irrelevant skill for IMers to have. Leave design to the designers. Even if you have a knack for design, I would suggest that you pay someone else to do it (unless you really really want to do it :P) because you could be doing something profitable instead of tinkering with Photoshop. Unless you have experience with Photoshop (or equivalent program), don't bother with web design. In the time that it takes you to design a mediocre e-cover or banner for example, you could have easily written an article instead (for example). That article could have driven a few dozen visitors to your squeeze page and gotten a few new subscribers onto your list.
That leads me into a fundamental skill that I'd like to add: time management. Hanging out on forums for too long is not work (haha...I'm guilty of this one). Checking emails is not work (guilty as well). You'll be surprised how much work you can get done in a couple measly hours per day.
If you want to build a business online as fast as possible, you'll need:
-a willingness to learn
-the proper mindset
-a strong desire to succeed
-100% confidence in your abilities to succeed
-good time management
Having these five things is far more important than learning about strategies or methods (e.g. list building, traffic gen, article marketing, etc.).