IC engine bearings are constantly bathed in cool clean castor oil (about 30% in the fuel). Tapers will need adjustment and some preload but not too much or they'll get very hot!
Workshop practise no 27?
http://www.rdgtools.co.uk/acatalog/W...CE_SERIES.html

Or, http://www.sherline.com/images/30100pic.jpg for $102, these are very good. Not sure what constant speed rating is but their a friendly bunch and will soon tell you. Morsed and threaded. Not as much fun as making it yourself though!

If high speed then I would be careful of the keyless chuck, if the spindle decelerates fast they can come undone (the chuck part), or fall off the spindle if threaded on and still doing max revs. You could use a small morse shank and a draw bar or a collet. Collet is much safer and far more accurate. At 3/8 side loads are going to be relatively low I would think so good quality angular contact (ie normal ones) should do the job.
Nice plane!