I would leave an inch or two from the pot's walls. And maybe 2 or 3 inches inner coil from outer coil. I am no expert but I think that if you come too close to the pot's walls you are not maximizing the contact surface between wort and copper. Also, if you are going to stir the wort with a paddle it's easier to get the flow going with a 1-2 inches gap.
I have used immersion chillers in the past, and I have always stirred the wort around it because it speeds up the cooling a lot. I found that annoying because you have to be careful to not mix oxygen in while you paddle. So I built a counterflow chiller. I like it much better because you don't have to "nurse" it: just open the valve and let the wort flow through it. Also I get MUCH better cold brakes which give a very clear beer without any filtration.
IMHO if you are going to brew for a long time, I think that the extra effort to build a counterflow chiller is well repaid over time. Costs about the same to build, maybe 20 bucks or so more.