Fairbanks is about as extreme as it gets in Alaska while still "on the road system". Shortest winter days, longest summer days, most extreme temps of any city Earth (-40F to +90F most years, sometimes -50 to +100). It's upsides include smart and interesting people because of the university, cheap land (by 48 state standards), getting to know the small community and people in it quickly, and the scenic beauty of Alaska.
Many people come here for the tasty critters as another poster alluded to, but non-hunters can be happy here too, if they are hikers, skiiers, or appreciate the scenery.
Sounds like you have some connection in Fairbanks. Anchorage is climatically easier, Kenai / Soldotna has more accessible recreation and fishing. There are Jo-Ann Fabrics in all of them and I'd definitely suggest you take the transfer, even if it doesn't include moving expenses. It is far easier to look for a new job if you have one than to be yet another newbie in town in need of a job. Plumbing, carpentry and electrical all pay well and if you are productive and show up each day, you can be busy most of the year. I'd suggest taking the transfer and then moving into the trades for the better pay.
The Park Service can be very picky - lots of people want those jobs. It's not a FL/AK thing. If that is your goal, keep your day job but volunteer with a non-profit, volunteer at Denali NP on weekend from Fairbanks or Chugach SP from Anchorage or Kenai Fjords or Kenai Watershed Forum from Kenai/Soldotna. Leverage that experience to internships or paid position and start to travel in those circles.
Fairbanks is a college town and there are bus routes. Anchorage also has regular city buses. GET A PLACE ON A BUS ROUTE. That is worth $100s/month in rent to avoid the expenses of car, insurance and gas while you can. Make friends, join the local outing clubs. Be the best damn carpooler you can when taking a hike with others (pay for gas, bring snacks, ask them about themselves, etc). I don't have a gun, a boat, or a truck, but I can get where I want because I'm many people's favorite guy to have along.
Also on housing: Whether it includes utilities is HUGE. Therefore, how well insulated is a huge factor in your costs. I knew a young married couple (both enigneers) who knew to rent the INSIDE apartment, surrounded by others on four sides. They never turned on their heat. They wore sweaters, and let their neighbors heat their apartment (because there is no insulation between apartments). A bit parasitic, perhaps, or maybe just the technically savy taxing the scientifically illiterate.