I think this is a hard question to universally answer because different people have very different priorities in life, but at the same time a house/apartment/condo/flat etc with absolutely nothing is very barren and unwelcoming.
I agree with others that the barest necessities are: cleaning supplies, basic tools (to assemble IKEA furniture ;) ), place to sleep, things to cook in, things to eat off of, things to eat with. Food. Places to store these things, if not built in, as needed.
My first (on-campus) apartment in college came with 2 beds, 2 desks, and a little couch (for 2 of us). There was NO storage in the bathroom, and the tub was very rounded so you couldn't even set things on the floor, so we got a tension rod with little shelves and a plastic drawer bin (not a necessity in many situations or people; but I wasn't a big fan of my feminine products sitting out or tripping over my shampoo :) ). For the kitchen I got a big (10"? 12"?) frying pan and a largish pot, a set of plastic mixing bowls with lids, whisk, spatula, set of 3 knives (Chef, slicing, paring), probably a cutting board, 2 plates, and 2 bowls. No wait, there were also 2 little plates! All the dishes were $1 glass ones. I had some mugs and my roommate had plastic drinking cups and utensils/silverware (don't bash the silverware ;)) I think she also supplied the can opener. That all suited us quite fine for a year. We probably had a broom and swiffer-style mop now that I think of it (I used it with a rag instead of disposable wipes).
More recently, when my bf and I moved 2000mi away ~18mos ago, while also moving in together for the first time, we knew our stuff might get here only after a while, so we packed in our luggage a kettle (to boil water) and a small wok (thought it would be perfect for 1-pan frozen meals and in a pinch could make pasta in it). We didn't pack any dishes or silverware so we got some food storage containers and plastic silverware we reused (but if you're moving in permanently you might as well get the real stuff!). We had ditched our twin beds in our previous locations and got a queen when we moved, so we had that. I think our cleaning basics were dish soap, dish sponge, spray cleaner, paper towels (rags if you don't have to transport them 2000mi!), broom, mop, floor cleaner, toilet cleaner, toilet brush. And plunger. ;)
After our stuff (including desk, table, futon couch, 1 low shelving unit, and books books books) arrived, our high priority items were: chairs to go with table, a lamp, a rug, a coffee table, and bookshelves. Some was thrifted or found secondhand, some we couldn't find anything we liked so we bought new (usually from discount retailers). A few things about us: we like to host/entertain, having friends over for dinner, board games, etc. We also host friends and family from out of town and guests from couchsurfing.com, so our futon sees good use. We like to experiment in the kitchen and prepare a variety of foods so we have lots of different cookware and tools that ALL gets used occasionally. Our walls are still mostly bare; but they're a nice brown color so it doesn't feel institutional or oppressive (Zebra would probably have the same effect! ;) Not that I support expensive wallpaper. Sleep on it. A lot. If you still want it in a month you can get it. ) I'm still dreaming that we'll pick out some artsy photos we've taken and get them printed up nice and hang them one day :) But that's probably after we move away from here... Also, my bf and I would both occasionally work from home, so we had an office corner set up, now he does so full time, making it that much more crucial.
Basically, your bare necessities coordinate with your lifestyle. But you don't necessarily need a dining table or a couch or a desk, etc just because everyone gets those things. Set up your place to make you feel comfortable and to support your lifestyle.
One last thing, that maybe should have been first: you are talking about setting up house (albeit, minimalist, at least for now) but also like you are looking at a future with your bf. I would advise being wary of duplicating too many items.