I suggest you start with a PSI Bolt Action or a Sierra twist kit and a Curly Maple blank. The Zodiac kit from ExoticBlanks is also very good for starters. All 3 that I have mentioned can be made straight-sided or with a slight bulge. You can buy a package of extra tubes so that you can practice your gluing, end-trimming, and turning. The Curly Maple is cheap and turns well and has a little bit of character. I haven't been real happy with the blanks I've bought from the company you mentioned. You can check the reviews on their website before you buy. Read quite a few reviews.
If you have some walnut, use that as it's a nice wood to look at, work with, and finish.
Edit:
I forgot to mention that the Sierra also comes in a push-button (click) version. I wouldn't start with the click kit because assembly is a little more challenging. Stick with the twist version of the Sierra (from Exoticblanks.com and many other sources), Gatsby (Penn State), Mesa (from Woodturningz.com), Manhattan (from Rockler; Craft Supplies USA also has a Manhattan but it is very different from the others - have never used it), Zodiac (from Exoticblanks; my favorite pen of this type), or Wall Street 2 (Woodcraft).
