For my $$$ I have always used 1/8" as the first size where I can start expecting a fairly true, non wandering hole, so I think finding, or making a base so your sphere is locked into a position where it can't roll away, so something with a like depression. Then if you have a drill press start drilling. IF you only have a hand held drill, then your problem for "straight" increases. Anything you can use to hold the drill straight will be helpful.
I have the Rockler drill guide, pretty good, but really costy. There are many on the market, you are looking for heavier build quality to increase it's ability to hold at a set angle, and offer you the best chance to drill straight.
Start watching this video at/around 2:45 mark to see a quick way to make a base for holding your sphere shape still.
