Ikea.

Depends on your aesthetic and your budget. Me? I could replace everything with IKEA and a good used furniture store in one weekend.

Practically, though, you should probably start with Sleepy's, because sleeping on the floor has got to be tough on your back after a while.

Craigslist.

Craigslist can be a gold mine -- even the free section. Try describing what you need in different way to get the most results. I search both "dresser" and "chest of drawers", for example.

Also try a Google or Yelp search for flea markets in the area. Some vendors offer delivery, car services have large SUVs, and a Budget van is only $20 plus mileage.

For tricky/special pieces (like a corner desk or specific sized bookcase or special material table) I do a Google Shopping and Amazon search which gives back a good sample of styles, availability and price range.

I just moved and am ridding the house of the 5+ year old Ikea junk, so I'm doing a lot of searching from work PC. Hope this helps :)

I had to do this recently when I bought a new house. My advice is shop, shop and then shop some more. Figure out what you like and compare prices. Check the sales flyers, too. That's how I found what I ended up buying.

Craigslist. I'm in a university town, and when the students leave after the end of each semester, it's a goldmine.

Garage and estate sales. This is the perfect time of year for it and you won't be supporting furniture companies that are deforesting the planet.

You need something to sleep on, something to sit on, somewhere to put your clothes and someplace to eat (could be a counter or a coffee table).

Buy things to fill those needs first from Ikea and then start filling in the other pieces more slowly and deliberately using Craigslist, vintage stores, furniture stores etc.

I'm facing this same issue moving out of a rented room into a full condo of my own. I've scoped out the best used furniture stores in my area, the salvation army, and through craigslist I've found a couple of furniture warehouses nearby that have a showroom open to the public with scratch and dents, showroom models and returns for insane prices. Search google in your area for furniture outlet locations nearby also.

When we moved, we had some furniture that was in too bad a shape to make the move with us. So, while we house hunted, we visited furniture stores. high end, low, mid, Ikea, unfinished, consignment, etc. "just looking" and pushy sales people leave when told- "browsing, no house/no contract yet".
Where you live determines sizes and placement. Budget determines the rest.
Since you have a clean slate, measure, then roam the stores. Think about your budget and tastes. Buy with thought.

Overstock.com has a great selection. I bought a wonderful mattress from them. But some of the sofas are too awesome and the shipping cannot be beat!

Oh no! Also, potentially, oh yay! Start small and build over time. You'll find things you love that way. But seriously, start at IKEA and get the essentials, like a bed, a table, some bookcases. Get a couch you love and fill in the rest over time.

Start by going through design blogs and saving the pictures you like the most. Once you have a semi-coherent look you want to go for get the major pieces (sofa, bed, etc). Pick the other things up gradually -starting over is a great chance to have all of your things work well together rather than the typical collection built up over years or decades.
The stores depend on your area and style. If you're near The Dump (thedump.com) they have a huge variety, many styles and all marked down a lot. But online try overstock.com, cb2, crate and barrel...

It depends on whether you're obsessed with design or not. If you really like looking for furniture and choosing the exact perfect piece, then skip getting "temporary" furniture. Only get a mattress, something to sit on, and a couple of folding tray tables; save your $$$ to buy special pieces one by one.

If you're not design obsessed and just want to have a comfortable home, then hit Ikea and Craigslist, as others have noted.

If it were me, I'd buy a few cheap, simple pieces from IKEA and thrift stores first. A table for eating and work, a comfy chair and/or couch for hanging out in, and a bed for sleeping. Those will hold you while you take your time to find nicer things that you love.

Not sure what city you're in, but my friends in New Haven, CT swear by a store called Hotel Liquidators that resells used hotel furniture. I imagine there are similar places in other cities... you can even furnish whole rooms at a time through them!

Only buy things you intend to keep. If you must buy a temporary fix, buy second hand. In this day and age, nobody should be buying cheap crap with the intention of replacing it soon.

As the Munchkins of Munchkinland would advice, it is always best to start at the beginning...

As much fun as it seems, I just can't get int running down Craigslist and classified items. Seems I spend more time and energy that the money I save is worth. And green options are quickly out weighed by the fuel used running all over time. I say, so the the resale district of your town and choose a few good basics. You can fill in as time goes...

This is a great opportunity to refine your style or explore a new one - what a great adventure you'll have! I'd start by buying a decent bed & sofa, go for quality & comfort, and then start hunting CL, flea markets, antique & secondhand shops (depending on your style). I've seen some amazing things on CL lately and most stores are having significant sales since the economy's still wobbly. Honestly I'd start almost anywhere but with that ad - that furniture's so ugly it's oooogly.

One more thought, if you have favorite retailers, call them and ask when they're having their best sales and/or selling floor models - you can choose something you love and plan ahead to get the best price.

Costco for a mattress, then IKEA for basics. That'll get you set up in a weekend with cheap-ish basics. You can then sell your initial IKEA purchases over time as you replace them with serendipitous finds. Also, West Elm is having some great sales on bedding these days.

High end furniture stores often have a scratch & dent collection hidden somewhere in the back. Dont be afraid to ask. I went to one store that had a goldmine in their basement, but you had to ask, they werent advertising it.

Also, www.worldmarket.com has fantastic things for cheap!

I wouldn't waste my money buying ALL new furniture (except a new mattress). Check craigslist, thrift stores and antique shops. Make sure to double check for bedbugs before buying though.

It would help if you tell us what part of the country you are in ... locals might have some good resources for you!!

It would depend on your style and your budget. But yes, at a minimum bed, dresser and couch all available at Ikea. Also if the possibility of another overseas move is still an option in your life I would not spend a whole lot of money.

In an ideal world-- one in which I'd invested in Google stock early on-- I would furnish my home entirely with pieces from Room and Board.