Safety first, you should get a decent face shield, one that is rated for impact from flying chunks of wood. Most of experienced turners will support this since it gives you a lot more protection than just safety glasses.
For a chuck, you can usually find some decent prices on amazon.com, and I can personally vouch for the NOVA midi chuck being a good purchase. You'll definitely want one for doing bowls, and it really expands the options for what and how you can turn stuff on the lathe. Along the line of turning bowls you'll need to get a nice bowl gouge. A round nose scraper is nice to have as well and will serve you well in doing some finishing cuts on a bowl.
For doing pens you'll need a pen mandrel so go ahead and plan on buying one. An upgraded live center for your tailstock is nice, but not necessary. There are a lot of different opinions about what tools to use for pens, I'll let the more dedicated pen turners comment on that.
Sand paper, and lots of it! Good luck!
I want to die quietly in my sleep like my grandfather, not screaming in terror like the passengers of his car.