Welcome and good luck with your first batch!
Mid-sixties air temp should be ok for brewing, the fermentation process releases heat so you'll be a little higher than that, but it should be ok. Depending on the yeast strain you use, sustained mid-fifties could shut the yeast down. But it if does, you can just move it back into the house. Another option would be to put your fermenter into a large bin or cooler with water and swap out frozen bottles of ice as needed. A floating thermometer helps you know whether to add more ice or not. But your plan sounds fine to me.
As for cooling your wort, I don't have any good ideas, other than no chill brewing. If your fermenter is well sanitized, then transfer the hot wort to it, seal it up, and put it in the basement or wherever you will be fermenting. Let it sit overnight and reach room temperature, then pitch the yeast. If you do some searches on the forum, you'll find info about that. Never done that myself, so am not speaking from direct experience, but others do it successfully.
Good luck with your first batch!