If you haven't bought the vehicle yet, I would reconsider. A better bet would be a pickup, Ford Ranger or Toyota in the small class, Chevy or Ford in the large size. Mostly because the more you can carry the better you'll be prepared.
If you do have the vehicle already...
rear locker - only problem that's hard to get used to is driving in curves on ice. Rear end will want to go one way and the front straight. I've had the EZlocker in mine. The do make the ARB locker now for the Samurai, but it is pricey.
small lift - shackle reversal will help smooth out the ride a bunch and is affordable. I have a used S/R lift that I can sell you, email me if you're interested. Will lift you 2" over stock. Most 3" spring lifts out there are going to be stiff.
small aggressive tires - your choice, mud terrain or all terrain. Stay around stock size or slightly larger, nothing bigger than 235/75x15. Anything bigger and what little power you have will be sucked out of your vehicle. Make sure you have at least one spare, plus a way to plug holes, plus some sort of air compressor. All terrain will probably be slightly better in the snow than the mud terrain. I've used both (not in heavy snow though) and prefer the mud terrain.
good shocks - will help smooth out the ride appreciably
exhaust - get a freer flowing exhaust on there, #1 improvement in performance IMO.
If you can afford it get your transfer case regeared. This will correct for slightly taller tires and make the Sammy much easier to drive off-road.
I can definetly recommend the bumper from Wheelers off-road. Very sturdy (smacked into a tree and didn't dent the bumper.) Not to expensive.
That would be it on vehicle enhancements on your budget. After that it would be outfitting.
Get a hi-lift jack, well worth the investment.
A hand winch, 2 ton rated or more, and not the cheap ones either. Have had one in my sammy for years and only used it a couple of times. Cheaper than an electric winch and just as handy.
http://www.roadlessgear.com/powerpuller/
Straps/chains/etc
first aid kit - you'll want a pretty complete, yet compact kit. Get some first aid training if you have none.
survival kit - up to you to decide, fire/shelter/water/food are the four basics. Carry it all in a back-pack so you can be mobile if needed.
communications - CB/HAM/shortwave the more the better
You'll want more storage space. They do make roof racks, and 1/2 racks, storage lockers, locking center consoles (good for securing handgun). Or you can fabricate yourself, I had a good size wood box in the back of my Sammy for the longest time. Dont forget about ammo boxes, good for keeping things waterproof.
Spare parts - I would carry at least 1 spare hub, alternator, fan belt, hoses, oil filter, gas filters, ujoints and every fluid. You're not likely to be able to get some of these parts in remote AK.
Gas - as much as you can carry.
As far as sun visor mounts go, forget it, not enough room up there (unless you have a small carbine). Depends on how handy you want a rifle. You might think about an ATV type mount in the back. Or something that will mount it behind the front seats (also a popular place for the hi-lift jack.)
I have had a plywood board mounted between the two roll bar extensions. Handy place to put a map pocket and the CB radio.
Most of all I would find some local Zuk-freaks and hang out with them. Get to know how your vehicle handles off-road. Go for reliablity first, then performance, then looks.
popular Zuk hangouts -
http://bbs.off-road.com/wwwthreads//postlist.pl?Cat=&Board=offroadsuzuki
http://www.izook.com/toc.htm
Some popular vendors -
http://www.petroworks.com/
http://www.northcoastoffroad.com/
http://www.zukisouth.com/
http://www.rocky-road.com/suzuki.html
http://www.hawksuzukiparts.com/
http://www.puresuzuki.com/samurai2.htm
http://www.breezeindustries.com/suzuki.htm
http://www.wheelersoffroad.com/
my home page
http://www.geocities.com/keithm_home/sammy.html
Hope this helps.