How long are your days?
You can grow plants under flourescent lights indoors, but you need to
rig it so that the lightbulbs can be raised as the plants grow and
maintained about 2 inches above the highest leaves.
Lettuce is a good easy plant for short days but even that requires 6
hours of 'sunlight'--I'm not sure if you have that in Anchorage this
time of year. You can make a wood box garden about 6 inches deep, 12
inches wide, and maybe 4 feet long (to be generous but small enough to
move), and grow lettuce, radishes, kale, and chard in it. Put drain
holes in each corner and one per square foot. Relatives of cabbage
and mustard, like broccoli, have taproots and can't grow in this setup
though. Radishes are small enough to work in this kind of box, and
there are also round varieties of carrots but these may be a bit
frustrating because the seeds are small and hard to handle and they
seem to take *forever* to germinate (up to 21 days).
I have an outdoor garden that I started in fall (california--no snow).
This is the first year I've grown vegetables. The lettuce was great
until it molded under flooding rains. Radishes seem to be pretty
bulletproof and are gratifying because they mature in a little over a
month. Of course it is hard to say how they'll adapt to your short
natural sunshine supplemented by flourescents to extend the day.
Day length is important. Be consistent in the amount of supplemental
light you give or your plants won't know if they are supposed to grow
or flower or what. From what I read, anyway.