For a clean pump and fittings, no teflon tape is required.
For dirty parts and fittings, teflon tape is not advisable.
If you can't clean dirty parts, you need to buy new ones.
Teflon tape should definitely not be used on inverted flare fittings.
I would be looking for a pump which the top half is held on with screws rather the ones which are mashed together with hope and prayers. I like the glass top ones personally.