The most common sized hole in a homebrew PCB is 1mm.
This is because the holes can be drilled using a number of different drills and drill bits.
An Archimedian hand-drill gives great control, but they can be quite slow to use. Stick a 1mm HSS drill bit in the end and carefully place it in the centre of the pad on the PCB. Hold the collar near the head of the drill in one hand and push down on the "top" of the drill with the other. The Archimedes screw causes the drill bit to rotate quickly, creating the drill hole.
While it does allow for high precision, the hand-drill approach can be very slow (if you have a lot of holes to drill the squeaky noise can become intolerable!). Drill bits as small as 1mm can easily be found.
You can use smaller drill bits, but with a hand-drill they're quite prone to breaking. The thinner the drill bit, the more accurate you need to be in maintaining a perfectly vertical up/down stroke. We've generally found that less than 1mm means lots of broken drill bits!
Our preferred method for drilling is with a Dremel-like rotary tool. These can take smaller drill bits than a hand-drill, since the shank can be as large as 3mm, while the cutting part as small as 0.1mm in diameter.
For these drill bits, you really should use a press, to ensure that the bit goes in and out of the PCB at exactly 90 degrees (even a slight angle can snap a thin drill bit easily).
A drill press is a really handy tool - but can slow down your drilling too. Not quite as much as a hand-operated drill, but can still make drilling slow and tedious. We use something of a half-way house solution; it's a Dremel drill, with a "snake-head" attachment, to allow you to move the drill-head easily, without taking the entire weight of the Dremel.
Without the precision of a drill press, we found any drill bit smaller than 1mm diameter would break too easily. So when we design our circuit boards, we try to ensure that PCB pads are at least 2mm and that hole sizes are up to 1mm.
Once the board is drilled, it's ready to populate with components!
If you like, you can trim the board down further, to make it as small as necessary. With the copper etched and the toner removed, the board can withstand slightly rougher handling than in earlier stages, so we tend to cut our boards to size only after all the other processes are complete.
Now go wash your hands.
If you can bear to use (and can find big enough) latex gloves, by all means use them. Messing about with Ferric Chloride is a messy business. And all too often leaves you with filthy-looking "ferric fingers" that can last for days!