A friend of mine started turning pens a while back. and it cost him $600 to get started.
He bought a Small but brand new lathe and turning tool set. (He shopped hard for good prices though) bought the drill bits he needed for the half dozen pen kits he was interested in. We found him a garage sale band saw for around 50 bucks or so. and the rest went into finish material glue and the extras.
he also bought a couple of nice boards from a local woodcrafting shop and traded blanks for kits.
he did already have an old drill press. And i am in agreement with other comments here. put you money in a good chuck and drill on the lathe. you won't be sorry you got a chuck and it is getting more use out of your lathe while starting up. this also means you need the drill chuck for the tail stock. I think you can get good ones for around 25 dollars but it has been a while since i have looked at them.
the harbor freight 115 piece titanium bit set is the best way I know to get most of the bits you will ever need. anything larger than 1/2 inch you will still have to buy as individual bits though.
A way to sharpen your turning tools and bits cannot be over stated. turning tools will need to be sharpened after making your first pen. if not right out of the box. even an oil stone will work but you must have some way to keep them sharp.
but for completness here is the list of tools i use in the order i use them in making a pen.
Small 6 inch metal ruler
pencil
Square
band saw
drill press and drill bit
sandpaper to rough brass tube
Glue (gorilla glue or CA are two favorites) to glue tubes in blank.
barrel trimmer or end mill ( some use these bay hand, others in an electric hand held drill I use my drill press again.
Lathe
pen mandrel (7mm or A mandrel works for more kits)
bushings for the pen you are making.
turning tools. 1/2 inch spindle gauge thin parting tool are a must, others are nice and make the job easier but you can get the job done with just these two.
sharpening machine and jigs for my turning tools.
sand paper, 150,200,300, and 400 grit.
CA for a finish
micro mesh, full set of all nine grits
friction polish
half ton press to assemble the pen. (You don't need a half tone of pressure but press needs to be large enough for pen to fit in it, wish I had spent 10 bucks more for one ton press)
trade secret for wood to protect the shine I worked so hard on.
and last but not least a pen box to keep it looking good in.
That is what I use on any pen. there are things I do at times that require more than this list.
you don't need all the tools I have listed but all the jobs need to be done.
good luck and spending time shopping for deals is well worth it.