There are lots of ways to do it, depending on how much effort you want to put in to it, what make and model control you have, and what your cutter is capable of.
You are right that attempting to start at the center with cutter compensation active without giving the control a large enough radius to avoid overlap will be troublesome. However, if you mill/drill away at least a cutter diameter in the center during your plunge, then your first circle can have a programmed radius twice the cutter radius, and still only have a 50% width of cut.
The approach you take to cutter compensation lead-in will depend on your make and model of control. Some controls can start comp with a zero-length move; some require any non-zero length (say >= 0.001"); and some require a move at least as long as the cutter radius or diameter.
Supposing that you need a long lead-in; that the final pocket diameter is more than twice the tool diameter; that you can plunge straight down with your tool (e.g. 2-flute end mill in easy-cutting material); that you want to approximate a spiral out; and that you want to climb mill the whole thing:
Rapid to pocket center, Z clearance
Feed Z at plunge rate to cutting depth
Activate comp left (G41)
Feed to one cutter diameter X+ of pocket center
CCW arc (G3) 360 degrees (this may take multiple lines, depending on your control)
CCW arc approx. 90 degrees, to X center, Y center+diameter+1*stepover
CCW arc 270 degrees, to X center+diameter+1*stepover, Y center
CCW arc approx. 90 degrees, to X center, Y center+diameter+2*stepover
... Repeat 90/270 until within finish allowance, then spiral out to finish dimension
CCW arc 360 degrees, ending at 12:00 position (X center, Y+pocket radius)
CCW arc 180 degrees, ending perhaps halfway to 6:00 position (X center, Y-pr/2)
Cancel cutter comp (G40)
Line back to pocket center
Rapid Z back to clearance
For the spiral step-out moves (approx. 90 degrees, from 3:00 to 12:00) use the radius that you are stepping out to as the radius of the arc.
E.g.:
...
G0 X0 Y0 Z.1
G1 F6 Z-.125
G41 D1
G1 F12 X.5
G3 I-.5
G3 X0 Y.75 R.75
G3 X.75 Y0 R-.75
G3 X0 Y.99 R.99
G3 X.99 Y0 R-.99
G3 X0 Y1 R1
G3 J-1
G3 X0 Y-.5 J-.75
G40
G1 X0 Y0
G0 Z.1
...