Philip and Boku have already covered most of the bases, but here are a few more details that come to mind:
I lost my manual and, thus, fiddled blindly with the camera settings.
I
strongly urge you to pick up the Magic Lantern instruction book for your camera. If at all possible, work your way through it before your trip, so that if you have any questions, you can post them here.
Nikon N75
Sigma 28-80mm f/3.5-5.6
Sigma 100-300mm f/4.5-6.7
I'm not intimately familiar with the Sigma lenses you have, but the only problem I would expect is that your resulting film frames might be a tad soft when printed larger than 8x10 or so.
I also have cheap Samsonite 2600 tripod that I haven't used but fear is too flimsy.
Even in strong daylight, shooting at focal lengths longer than 100mm without a tripod is a recipe for serious blurring. The traditional guideline is that your shutter speed needs to be faster than the reciprocal of your focal length - for example 1/300th sec or faster if shooting at 300mm - but a tripod is by far the safer route.
I have a few seemingly useless filters besides an "Optica High-Def Polarizer" which doesn't even seem to exist when I try to research online.
Forget about filters until you master the basics.
I believe I used Kodak 400 speed film which was processed by CVS (not 1-hr.)
If you were using print film (negatives) and you are judging your results from mass produced prints, that might be your main problem right there. Nothing can kill a good image faster than an auto-everything photo lab print. Both the white point and the black point are typically clipped, contrast and saturation are cranked up, little effort is made to eliminate colour casts, etc.
Finally, as I continue to read and learn, it seems I might be best prepared with a wide-angle lens and a new polarizer when in Iceland.
28 is already quite wide for a 35mm camera. I think you would be better served waiting until you can get consistently good results from the 28-300 range you already have before going further afield. (Most ultra-wide lenses like 17-35 are sold for use on dSLRs, attached to the majority of which they effectively become 25-52mm lenses.)