There are two ways the grease fittings go in - the ones that press in, and the threaded ones. I don’t recall off the top of my head which the front spindles are, but if they are threaded it is 1/8-27 NPT (tapered pipe thread). Proper drill size is letter R drill.
If they are press in then there are special drivers available from the vendors to help you install them without deforming them.
Also, when you install new bushings, be sure the holes in the bushings line up with the holes in the spindle so the grease has somewhere to go.
No, 1/8" pipe thread tap is quite a bit larger than 1/8" diameter as BobC suggests.
Someone correct me if I'm mistaken, but aren't the press-in fittings 5/16" diameter hole? But you need to be very careful, if you oversize the hole by wobbling the drill then the press-in fittings won't stay pressed in. Best to carefully remove the old fittings and then press new ones in without drilling. If the holes get so chowdered that the press-in fittings won't stay in then you can overdrill with the R drill and thread for screw-in fittings.