Well, it depends on your reasons for mining in the first place. If you just like the idea of bitcoin then that's one thing, but if you are trying to make a profit, you want to maximize your cost / generation. This means either as many cards as possible on one rig or as cheap as possible multiple rigs.
For cases there is what I suggested, the Rosewill THOR, it's fairly reasonably priced (if you can find it) and has 10 expansion slots, enough for 5 cards if you space them properly (they will be cramped and hot though, and it has only ok airflow so you will need to set up some fans). Another option is a tech bench, mostly open air. You can also set up a rig like the one in the picture you list, except that the side card will block airflow from the sides getting to the crammed together cards on the motherboard. You can also get an HAF 912 (again, poor air flow, smallish case, but has 8 slots for some reason) for very cheap, an HAFX (huge case, lots of airflow, kinda expensive) which has 9 slots to uncramp things a little bit. Only the antec nine hundred TWO (v3) will be able to accomodate 4 cards, and it would do an okay job of it I suppose.
3 cards will fit in almost any case though, 300, 900, 1200, Lian Li k57, etc. But again, when you are building a rig you want to maximize the number of cards you can fit into a single rig, or else cheap out as much as possible on multiple rigs.
Another nice option that is in between cased and caseless are what are known as "Tech benches". They are basically open-air but fully rigged up cases. One example I've been looking at would be:
http://www.amazon.com/MYOPENPC-Transparent-Acrylic-Station-motherboards/dp/B004TZ56GU/ref=sr_1_13?ie=UTF8&m=A3Q4NSDXS8U7OP&s=generic&qid=1306788458&sr=1-13I'm still trying to work out which ones would best fit the most cards though.
