If you're talking your own mooring with a mooring permit, you need to go through the Harbormaster's office:
http://portlandharbor.org/mooringappmaster.htm
Bad news is that it looks like the area near Bug Light is "closed." Other areas have waiting lists. Get on the list now, as it could be years before you get a permit.
I don't know if any of the marinas there offer moorings as well as slips or not. I have never heard that they do, but I'm way up in Freeport so I'm not a good judge of that.
As for the cost of the stuff, when we got our mooring 15+ years ago, it was about a grand for the 5000# granite block, chain, shackles, and ball. Probably more than that now. Our permit is around $150/year and maintenance is probably another $150, depending on who you use. My husband pays those bills so those are just guesses. But still, even with that initial expense, the mooring costs just a fraction of what a slip would cost.
How do you plan to do parking and shore access? That's not always very easy.