No matter the "main zone" you start with (cheek or neck) I suggest you to begin sooner as possible the upper lip. It's pretty much the must sensitive zone of the body when doing electrolysis (even more than pubian zone). So as you probably won't be able to handle much in one time (especially if your upper lip hairs are thick), starting it soon will permit you to do smaller zone for less pain.
If they got a good quality laser where you go and you got dark hair it works pretty well to weaken the hair but laser rarely get totally rid of hairs. You may expect good results if you start by 3 laser treatments then start electrolysis. You will save a lot of money with few "good quality" laser treatments. Electolysis usualy takes over 140 hours for thick hair (over 8000$ for most of peoples). Laser, if working, may save you about 60-70 hours of electrolysis (about 4000$) for 3-4 laser treatment (about 800$).
Laser will often fail on unequal hairs, if your hair seem to "split" color when they grow you probably won't want to waste money on laser.
But really, start the upper lips soon while doing the rest. Upper lips tend to lose pigment easier than the rest of the face so by doing small zone you may avoid harsh and discolored skin.