[lstool]

Yup,
Drill bits you are using are fine and center drilling is fine (and center drills are not designed just for centers on a lathe) if using a jobbers length drill using a center drill first would be normal & proper proceedure to start the drill on center of the desired center location accurately(Center drill) (hence the name) so I will have to disagree with WMS on that issue.
Try this as you are drilling by hand (as I am sure you cannot establish a given feed rate unless you are a robot and can regulate you hand accurately) increase the feed by hand untill the chatter stops you need to load up the tool right away, also make sure when center drilling let the center drill establish a diameter slightly larger than the drill by at least 1/32 or so.
To advoid all this and to speed processes (Time is money) up I use cobalt stub drills 135 deg. split point. Once you start using them youll wonder "Why didn't anyone tell me about this before?" it eliminates the need to use a center drill as you do when using jobber lenghth drills to drill a hole accuratley. And that web on the tip of those drills what a pain in the neck. I remove them by hand, all of them I have a special way of grinding them out nicely.

A little shop trick... WD40 work as a great lubricant for machining alluninum, drilling & tapping

So by the way the proper speed & feed would be...1528 Rpm's feed would be .005 per rev or 7.64 in. per. min

Just a thaught
Lenny