My advice ... don't start with slimlines ... for beginners they are too hard to do well on the first few attempts. . They are not inspiring. . Do something that you really want to do.
In my opinion, best to start with a 30 Caliber Bolt Action pen kit ... considerably more expensive but worth it to have a virtually guaranteed success. . Before you tackle the kit, get some extra tubes and practice, first with wood as the blank material, and then with some of the cheaper acrylic blanks. . I would actually suggest Alumilite blanks if you want to spend somewhat more ... Alumilite is easier to turn than the acrylics.
The reason for the 30 Caliber Bolt Action is that it is a single barrel pen kit (slimlines have two barrels ... so double the trouble). . Also, the 30 Caliber Bolt Action is naturally straight-sided ... so somewhat easier to shape and get an attractive result. . Furthermore, the Bolt Action result is somewhat novel ... so you are inspired as you work . . (Slimlines, until you know how to handle them, are really pretty "ho-hum".)
An alternative to the Bolt Action is a Sierra or Gatsby (or similar ... there are several). . These can also be turned straight-sided which is easier in the beginning ... and they are single tube pen kits so you get to your result faster, which is important in the beginning. . There are quite a few kits which resemble the Sierra/Gatsby and are cheaper. . So look around and ask around ... someone may suggest but I would go with the Sierra twist. . As I said, there are look-alikes which are a little cheaper but I don't think you should make price the deciding factor ... buy the one(s) you like and get inspired right from the beginning. . Have a look at the Aero kit ... it is really nice looking ... even nicer than the Sierra. . But it costs more.
You can buy packages for the Bolt Action which includes drill and bushings. . Same is true of the Gatsby.
Happy turning !!