Most of the responses you've gotten we've very good but I would differ on just a couple of points.
1) Most deadbolts are 2 1/8". There are a few that are smaller (some schlage come to mind - but even they came with adapter rings so you could use them in a 2 1/8" crossbore)
2) Use lipstick but you don't have to buy it. Women buy it all the time and then they decide they don't like it (the color). Just ask. You'll get all you need for free. Most of mine comes from my Mon. (Wife doesn't were it -and I'm glad - it tastes like crap!)
3) If you don't have a jig use the paper template that comes with the new lock. First (using a center punch -preferably a spring loaded one), mark the hole on one side of the door and the hole on the edge of the door. Then
***without moving the centerpunch out of the mark for the edge bore***
, rotate the template and mark the outside whole. (Don't forget to compensate for the door's bevel if it has one)
Next, using only a 1/4" bit (not the holesaw yet) drill halfway into the door from both sides. Your (pilot) holes should match up. Then drill the pilot hole for the edge bore. After that, use the holesaws and the pilot bit will follow the existing holes. With practice you won't need the drill pilot holes first, but for now it will be much easier (and if you mess up, the mistake will be much easier to correct).