After you make the big changes, then you can start looking into things that will save you incrementally (~$20 a month). What say the others about this?
I agree to an extent, it certainly makes sense to focus on the big changes. But that doesn't mean you don't act on all fronts at once, just that you prioritize. You learn a lot as you go along, so don't focus on perfection, and don't "spend money to save money", especially at first.
I use the universal grooming device method and it works well for me, though I still do a little trimming shave in the shower. A cheap blade lasts 3-6 months this way.
Drying on a line in high humidity is possible, but something thick like a feather mattress isn't a good example. Start with your normal thin clothes and see how that goes, they should dry just fine. Hang your thicker stuff out to dry for while to get most of the moisture, and then finish whatever clothes you need to in the drier to get the rest.
Dishwashers aren't bad, they are just dishwashers. I think there are a lot of things that are not inherently good or bad, but we should be well rounded rational thinkers and able to figure out for our situation what is the best use of our time, money, and valuable resources. But sometimes it's not obvious, in which case it helps to get the opinion of other like minded people. If you share specifics of your situation I'm sure we would be glad to chime in with stronger opinions... :)