Mordokai, enjoy Alaska! I lived there for 5 years and it is beautiful. I was stationed in Anchorage with the Army. I lived both on base and off base during my time there. Public transportation is limited and VERY expensive, renting a car is the way to go but can be pricey. There are tour buses that go up into Denali, but your best bet is to take the train from Anchorage then hopping on a tour bus in Talkeetna. The train also goes south to Seward on the Kenai peninsula where you can go on a Fjord boat trip, see some glaciers, puffins, sea lions, sea otters, and maybe a whale or three. While in Seward you can go on a dog sled ride from one of the pro's. He has a training camp down there. They have sleds for both snow and dirt and I seeing puppies is always cute. I never made it up to Fairbanks but I have a cousin who is going to school up there. Being a smaller city it has less to offer but your chances of seeing the northern lights does increase. Anchorage has too much light pollution to see them clearly even on a cloudless night.

Word of warning, September (especially late September) brings on some colder temps and chance of snow, dress appropriately. If you enjoy fishing you are missing prime Salmon fishing in the rivers, also a simple walk on a trail in the woods is not so simple, be aware of your surroundings. Bears, wolves, and moose are common even in downtown Anchorage (maybe not the wolves but two active packs were on base when I was stationed there and they did attack dogs and people...)

As to what to wear, comfortable boots, and clothing to match the conditions. Layers are helpful, you can always remove or add a layer if you bring enough. Mosquitoes are still an issue in September, as well as ticks if you go too deeply into the woods. Cell phone reception is spotty the further north (or south) of Anchorage you go until you are closer to Fairbanks. Juneau is not a realistic destination unless you are part of a specific tour group. Those tours include a train ride to Denali and Fairbanks, a flight back to Anchorage or possible Seward, then a boat trip to Juneau and then back to the lower 48 or Vancouver BC usually. A decent coat, hat, possibly gloves if necessary. You can always buy appropriate clothing if necessary, it is plentiful in Anchorage (touristy stuff).

Lots of excellent places to go to eat in Anchorage, seafood is still pricey but abundant. Some things like fruit and milk are VERY expensive (no local dairy farms in Alaska anymore). Also some chains of restaurants have no presence in Alaska at all. Coffee shops are abundant and small coffee huts are on almost every street corner. I recommend Kaladi Coffee at the New Sagaya Market. Do not be surprised to see Salmon or Reindeer sausage as toppings on pizza.

Unfortunately I am no longer living up there and all of the people I know who are still up there either live on base (they are pretty picky as to who they let in) or are struggling college students living at the University who do not have the nicest of roommates...sorry. I hope this helps in your adventure in the frontier!