A single rabbit or pair of rabbits needs *either* 24/7 access to 60+ square feet of space (a "run" area attached to their cage with playpens, for example) OR at least 4-5h outside the cage each day. Bigger is always better with cages unless they're free-range all the time (like a house cat), though the more time they spend out, the more you can scrimp on cage space.
An important thing to consider is that rabbits are most active around dusk and dawn - they don't sleep all night like most people do. Mine are usually awake and often bouncing off the walls at 3 am, to the point that they seem almost as nocturnal as my sugar gliders sometimes. In other words, if you cage your rabbit at night, you don't want him to be bored and destructive in a small cage.
While there's not a "minimum cage size" per se, ALL store-bought rabbit cages are way too small. Most people who want a cage build one themselves with storage cube grids (aka a "NIC condo" or "C&C cage"); some opt to convert a large dog crate or just fence off an area with pens.
I also live in a 2bd apartment... we've sacrificed a large portion of the living room to fence off a run for my rabbits, but that's not practical for most people. We tried free-ranging them, but they bullied the heck out of the cats, peed on ALL of the cats things, ate the cat food, camped out in the cat box (I use pine pellets in it just to be safe, since almost all cat litters are unsafe for bunns), etc. Our poor cats hid out in the master bedroom most of the time, helpless in the face of an evil little lionhead and her Holland lop side-kick. Since space is a concern for you, I'd recommend a NIC condo that focuses on height to get extra space. If you bunny-proof and litter box train, you can let him out for a few hours a day to avoid having to fence off a 60+ square foot area.
Here's the first NIC condo I built - it's 2 grids wide x 3 long x 5 high, so it only has a "footprint" of 28'' x 42'':
(I didn't have direct access between the first and second floors in that condo because they were never locked in it - obviously you'd need to leave a grid out so your bunny could jump up if the cage were going to be closed)
You can build a cage like that for around $110-$130. With grids on the bottom floor for added stability, which I did with that condo, it would require four boxes of 23 grids; however, I built a 2 wide x 4 long x 5 high condo at my boyfriend's apartment (I'm living at his apartment for a year while he finishes school and then we'll move back to my house 3h away) and I did NOT line the bottom floor with grids yet it's still plenty sturdy. Not using those six extra grids would let you eke by on three boxes of grids for a 2x3x5, saving you around $22.
cage info:
http://breyfamily.net/bunnycage.html
http://www.guineapigcages.com/cubes.htm (shows how to do coroplast floors if you'd rather use that than plywood)
best deal on grids for the cages:
http://www.sears.com/stor-floor-sta...p-00913332000P?prdNo=1&blockNo=1&blockType=G1 (do site-to-store for free shipping if they aren't stocked at your local sears)
I prefer coroplast (corrugated cardboard) for my floors, as it's cheaper than plywood and can be cut with a $1 pair of box cutters. Most Home Depots sell a 3'x6' sheet for around $14, which is the cheapest I've seen.
Also, dowels can really help add some stability to a big cage (they stop the floors from sagging) - Home Depot charges $3-4 each for dowels, which is a rip-off. You can find 3' long dowels in a large enough diameter for cage support at Hobby Lobby for under $1 each.
Home Depot (or Lowe's, etc.) is also not the place to buy zip-ties. HD is like $5 for 100 of the 4'' ties and $18 or so for 1,000. If you're lucky, you can find some in a dollar store (Dollar Tree, for example) that are $1 for 100. Failing that, you can find way better deals online than at hardware stores - for example,
I sell 500 for $3.80-4.05 (natural is cheaper than black for some reason) on my website; shipping for just the zip-ties wouldn't be more than about $2.
If you dig around with the search option on the forums, you can find lots of pictures of different condo and DIY cage designs - everyone does theirs a little bit different
.
Here's a good thread; I think there might be a new/2013 version of the thread as well.