Assuming that the lathe is the Portass PD5 you mentioned in another thread, when you tighten the tailstock clamping handle, it should pull the tailstock up against the angled dovetail side of the flat bed ways, so it will always clamp in the same position, so no need to worry about that.
But there is adjustment side to side to align the body of the tailstock with the headstock spindle if the centre drill is not drilling right on centre. The body of the tailstock and the base are two separate pieces, with an adjusting dovetail or step slide running sideways for this purpose.
Other than that, use the largest centre drill you can, at the highest RPM you can.
Use a good quality name brand centre drill. Not cheap no-name junk.
Use a pecking motion to keep clearing the chips and to keep the tip cool.
Flood it with whatever oil you have in the nearest oil can, to keep the tip cool and lubricated.
Don't try to drill the chamfered part of the hole to full depth on the centre drill. Only a third to halfway is needed to make enough of an angled face for the tailstock centre to engage with in use.
And as said already, forget centre drills for starting drilled holes. Use a spotting drill instead. Or a very large centre drill and just use the very point to put a small divot in the job to start your first drill proper. Reserve centre drills for when you actually need to use a tailstock centre in the hole afterwards.
Edited By Hopper on 09/09/2022 11:07:07