Jim,
You're already getting WAY too worked up! Expect to blow up your first set of blanks, and possibly your first few. This will probably be due to a few problems, including dull tools and poor glue joints/insufficient glue, but may also just be due to a good, healthy catch. It's just gonna happen, and you may as well accept it (I had a starter kit from PSI, and lost 50% of my half-blanks). Most of the time, this will happen after you've rough turned to a cylinder, and just as you're taking the last cut before switching over to sand paper. If it comes off in two or three relatively large chunks, you may be able to glue it back together using CA if you're careful, and any large gaps can be filled with shavings or dust.
That being said, my tips are:
1) Make sure you cut each blank slightly oversized so you can use a barrel trimmer, sander, etc. to square the blanks to the tubes.
2) Drill with a backer block until you get the feel for your drill press, this way you'll be less likely to have the hole shatter as the bit exits at the bottom.
3) Pick your drill bit size based on the glue you're using - if you're using CA, use the recommended size. If you're using Poly (e.g., Gorilla Glue), you might want to go up 1/64", since poly needs a little room to expand.
4) No matter how dry it may feel, Poly glue needs at least 8-10 hours to dry.
5) Remember to square the blanks to the tubes before you start turning (one of my most frequently overlooked steps)
6) Sharpen your tools before you start each pen.
7) Go slowly, and take light cuts.
8) If you have to press hard with the tool, it's probably dull or you aren't using it correctly.
9) One of my more controversial suggestions - start with a skew, and learn to use it. You'll be glad you did.
10) Since you're making slimlines, don't start with a "bushing-to-bushing" slimline shape. Start with one that doesn't include a centerband (see http://www.woodturnerruss.com) and give yourself a little more room to play. Slimlines require you to turn away everything but approximately 1/32 or 1/64" of wood, which doesn't leave you much room for errors.
11) Don't sand for too long. Heat is the enemy of most woods at the thicknesses we're working with.
12) Make sure you have some MicroMesh on hand.
13) Pick a finishing technique you want to try, and stick with it for at least five or six pens.
14) Be sure to post pictures of your pens and ask lots of questions!
As for what to try next, I actually don't recommend slimlines for the reasons I mentioned above. I like cigars for beginners because they look a little more impressive (IMHO) and they have more wood. So, cigars are a great next step, especially since they are pretty inexpensive. But, depending on your taste, you might want to try either a Sierra or a Jr. Gent/Baron kit next. The Sierras are nice because they are a single body, and the Baron/Jr. Gent pens are very classy looking. Spend your money on good quality platings, rather than the cheap stuff, and you'll be glad. I have a bunch of the cheaper 10K kits and I'm trying to decide how I'm going to get rid of/use them.
Good luck!