Leave it overhang, don't wanna press down, it may screw up the paint on the baseboard.
To add to this... It also keeps the splatter off the base when you don't tape it down to the base.
I use 1" tape 90% of the time and this is also dependent upon the style of base. 1" gives me more flexibility of following the wall. Some walls are not 100% straight.
If I use paper I'll apply it to the tape by hand (only when taping base, window trim or door trim). The tape gives the straight line and the combination of paper/tape screws that up so I like to solo the tape for my lines and add paper later If I need it.
I do have a couple tape applicators:
... I have only used them for commercial work and I MIGHT get one small commercial job in a year... so they sit around the shop... These are not very durable and are a waste of time and money to work with. Initially, they do a great job but I dont like to get my tape 100% against the wall.....
I do use a hand-masker in most jobs... but the use varies.