Make sure to spend some time and effort on the tailstock, too. On this class of machine they are notorious for being problematic -- not aligned properly, unstable base (causing wide variations in position) and so on. I found it most expedient to do some mill work to address the issues mine had, but a lot can be done with shims if you don't have the luxury of a mill sitting next to the lathe. Once aligned, I'm damned if I'm going to set the TS over to cut a taper, but that's just me.....
One alternative (and one I also have done) is to mount a drill chuck on your toolpost. I did it with a chuck that is mounted using a 1/2" thread. I had a boring bar holder that accepts 1/2" diameter shanks so it was -- almost -- a no-brainer. It can be real nice if you start with a small-diameter drill and work your way up, because the tailstock usually has to be moved back partway through the operation to accommodate longer drills. Not the case with a TP mounted chuck. However, that also is when I discovered my problem with the saddle gibs AKA slide plates -- the whole saddle would tip up and back when I applied pressure to the drill. One things leads to another.
BTW, if you're enlarging holes in brass, beware -- conventional drill bits will self-feed, or, worse, try to and then break. This problem is most apparent when using the toolpost-mounted chuck because there's nothing to prevent it from happening. Trust me: I know this for a fact. It's scary to see your drill bit sort of "unwind" when it catches, because you know it's THAT close to just snapping apart from the stress. And since a chuck mounted in the tailstock is just using the taper to hold it in place, it could be pulled out of the tailstock......so the fact that the TS has a feed screw isn't much comfort, either.
