I stripped the varnish off with paint stripper - it was a nightmare.
I found out later that it's supposed to be a better idea to leave the varnish and use primer on top, in case you want to return to the bare wood at a later stage.
As suellen says, it's a dreadful job... i used a little mini paint roller to get at the side of the spindles that were against the wall, but it's very hard to get all the angles correctly.