Lots of good comments. Just wanted to throw in my experiences.
A small starter kit may not be a bad idea. I would NOT go for the ultimate one though. Too much stuff you may never use.
After getting your lathe, I would buy a roughing gouge and a skew and a sharpening system to start. The tools can be Benjamin's Best from PSI or from Harbor Freight. Learn to sharpen and use those tools. After a few tries, it becomes second nature. Once you learn the basics, then look into the carbide tools if you want. Reason is the standard lathe tools are more versatile and IMO give a better finish if kept sharp. Get into the habit of resharpening before every pen or two. If the hobby sticks, then you can upgrade to better quality tools.
Turn any chunk of wood you can find. If you drill a 1/4" hole in it you can mount it on a mandrel without tubes, or turn between centers if that is your preference. Turn it and finish it until you get the hang of it. You can use pine, scrap from the shop, firewood, or branches that came down from the last strom.
The sierra kits are nice and easy. Probably a good place to start. But, you should also consider the slimline kits. Why? They are cheap. They are customizable to a large degree. You can do a lot of different shapes and styles; add a stylus, take out the center band, make your own center band, make a one piece, etc. They get you thinking about form and design. They are also a nice size to give away which you will want to do after you turn a few.
Another argument in favor of the slimline kit, anytime I bought a mandrel, it came with a bunch of slimline bushings and a 7mm drill bit.
Just my $.02. As someone else mentioned there are a lot of ways to get into pen turning and none of them are "wrong".