Welcome to the forum and to woodturning as well. If you work safely and have fun learning from others while doing what you like, you've joined a great community of folks. You've also posed a simple question that leads to a complex response.
Local clubs and organizations like AAW, forums like this one, online videos, and woodworking/woodturning related sites are great resources. PSI offers a couple of free DVDs, one pertaining to pen making. Many other vendors also offer helpful resources for free on their web sites. Often better than a public library, a local club may offer their own library of books and videos you'll benefit by reading/viewing.
A drill press can be handy not only for drilling pen blanks, but may also be utilized as an alternative to a dedicated pen press. So can a large enough vise (with proper jaw protection) or your lathe (by cranking the tailstock). Depending on your budget, IMO you should plan ahead, considering what else you may some day want to drill. Unless you start with something too small or underpowered, this may be the only drill press you ever purchase. Great savings can be found by checking CraigsList and other online resources for used equipment, or other reputable online vendors for special sales and closeouts.
Are you limited to benchtop models or can you accommodate a floor standing press? You'll want funds left over for other things (over time) like various types of bits and the drill chuck capacity to match the bit stems. Various clamps and vises are available to secure material to the DP's table, enabling you to drill more accurately and safely. There's even accessories to use your DP as a buffer, sander, or vertical lathe.
You may eventually need enough power in the motor to handle large diameter Forstner bits and hole saws. The range of speeds should go low enough to meet recommended rpm for the bit in use, one factor important toward minimizing heat buildup in the drilled stock.
OTOH (and I almost forgot to add this) you can often use your lathe's tailstock to achieve horizontally what you'd do vertically with a drill press. It's just a matter of matching up the right components.
Those are some general responses. Provide more data and you'll probably get lots of feedback specific to your decision making process.