Kudos for considering simple living. I relish my college days when I could move everything in one small pickup load— furniture and all. I'm thoroughly in the throes of empty nesting and shedding all the leftovers from a family of four to what two can use. I have a yard sale planned to aid the process.
I lived in a 20' camping trailer one year while in college (and and a couple others in my life). The furniture and appliances were all built in and hte extra bunks were perfect for storage. The Tiny House movement is the epitome of this process I think, and pretty much like living in my little trailer, decor aesthetics aside– camp trailers are like living in a Formica box.
I find the idea of living aboard a sailboat to be the ultimate. Houseboats are part of the Seattle housing mix. They were once the choice for the down and out, but now the moorage spaces are mostly condos and the hole in the water is worth more than the floating home.
I have proffered the "One Meter Cube" notion, where everything you own must fit in a one meter box. I came across the "100 Things" concept last Winter, that is the SUL version of simple living: you can own 100 things, period. If that doesn't get you honest, nothing will!
But to address your questions:
They real key is an informal lifestyle. Once you get off the fashion nipple, it's easy to live with simple cheap belongings. They are easier to acquire AND shed, but it won't look like the Ethan Alan catalog. It does parallel the backpacking philosophy in demanding absolute practicality and eschewing fashion.
Microwave/Oven: I think of microwaves as disposable appliances. You can buy used ones in thrift stores and yard sales for pennies and that is the ecological answer. I had a room mate who used a toaster oven in college pre-microwave and could cook anything in one. He was a hibachi master chef too, so don't leave out barbeque grills.
Washer/Dryer: laundromats and apartment laundry rooms are the first things that come to mind. That is a pain and not having laundry appliances usually means having more clothes to get through a week. But if you live in town, that is the way to go. Rental houses sometimes come with too. Your housing needs high current wiring or natural gas for the dryer. Washing machines are easier to fake into service: you can happily run one from a garden hose– hot water not needed, although you can just pour in hot water from your stove. The off-the-grid option is a tub and a laundry line, which sufficed for centuries. That implies wrinkles or ironing for cotton, although synthetic hiking clothing works even better and lasts longer with hand laundering.
Refrigerator: the old college dorm half-fridge seems to be the standard. And the microwave goes on top, of course. Our fridge went out last Spring and I can tell you that managing a household with camping coolers sucks. And I had a dedicated freezer to handle the frozen stuff and keep the ice supply going. A single person should do well with a tiny fridge. I'll bet any college neighborhood would have dozens available at the end of any quarter and a mountain at the year end.
Bed: futons with a folding frame to double as furniture. There are folk who hammock 365 and you couldn't ask for a more portable bed. Even if moving cross-country a lumber hammock frame can be constructed with a rental saw and Home Depot sticks in a couple hours, so you could leave it behind, or sell it on Craigslist pretty quick.
Furniture: I have said that if I were a single college guy, I would just buy patio furniture. Easy to find used for cheap, folding options, and perfectly comfortable. Those big plastic Cape Cod lawn chairs are ~$18 new and a great reading chair. You can even get matching footstools. I bought two with a folding table for $25 at a yard sale last summer. I had my morning coffee and a read sitting in one on the patio this morning.
Table: +1 on Ikea, and there is the thrift store and yard sale option. I got a great oak drop leaf/folding table for my daughter at a garage sale for $25. Both sides drop to allow it to stash in a space 1' deep x 3' wide x30" tall. I could easily get by with a card table and in fact I use a big round one in my computer room as my over-flow desk. About $10 for a really good one at Goodwill (if not less) and they will store anywhere.
Chairs: as above– Ikea/Goodwill/yard sale. Extra points for folders. I used to have a big bean bag chair that I'm sorry I sold.
Shelving: Ikea, "bricks-and-boards", plastic knock-down commercial style ones from Home Depot— or none. If you have the rest of your stuff under control, what do you need the shelves for? Big plastic storage tubs are the nomad's choice and if you are really doing it right, a couple duffel bags should do the trick.
Forgot my favorite bookshelf– they fold. You can get ones that have no top shelf and can be stacked using metal dowels to hold them together. I think I paid $10 for the one parked in my living room with the telephone and a lamp on the top and books below. Easy to get through doorways :)


And Vincent Van Gogh's bedroom in Arles– the epitome of simplicity (lined with $100,000,000 of Post Impressionist art):
