Corys... happier in a school?

Yes they do prefer to be in groups of their own kind, 4 minimum with 6 or more being better. They are MUCH more secure, visible, and active in groups.

6 should be fine in your tank, you might even be able to pull off a few more (they make great scavengers). I lost a couple within a 1 week period (No clue why) so now I have to replace them in my 55. Right now I have 4 but they school pretty tightly and they are really fun to watch. If you want cory's i would recommend a sand substrate to protect there front whiskers (barbs). They use these to detect food. If they loose those barbs they are pretty much goners. If you also want shrimp (make sure they are big enough the cory's wont eat) I would go with a darker substrate, maybe something like black sand. Cory's are scavengers and will eat just about anything. Personally, ive seen them eat freeze dried blood worms, flake food, micropellets, sinking pellets, algae wafers, etc. Shrimp are also scavengers and will eat a similar diet. Word of caution, if you are trying to breed shrimp, I wouldn't recommend putting cory's in with them. Cory's will eat their eggs if they can Good luck on your tank.

In a 40g you could easily fit 6-8 cories. For shrimp, the general ruleof thumb is 10 adult dwarf shrimp per gallon (for bioload purposes). If you are going with a species of shrimp that will multiply readily in the home aquaria (like cherry shrimp or other neocaridina) leave plenty of room for their growth. Glass shrimp should multiply, though some species of glass/ghost shrimp require brackish conditions for their larvae to develop. Another important thing when housing shrimp is to make sure your filter intake is covered with a prefilter (sponge, media bag, nylons) to protect any small or young shrimp from being sucked into the filter. Shrimp are omnivorous so will eat any prepared fish foods readily. The cories will love the worms, but you could also feed a sinking wafer (i like Ken's catfish pellets and Hikari sinking wafers for bottom feeders). The cories will love sand, shrimp are not particular about their substrate, though for the colored species I like a dark color as it helps to showcase their coloration. As for plants, that is determined by your lighting. Low light plants like java fern, java moss, crypts, anubias, some hygros, etc can do well in 1-2 watts per gallon (divide the total watts of your light fixture by the amount in gallons). The plants I named do not typically need ferts or co2 injection so are a nice place to start. Hope this helps!

edit: If housing inverts with fish its always best to quarantine the fish for a month first as inverts are very sensitive to most medications. You might choose to get the fish first and then a month later put your inverts in the tank. Best of luck!

All fish can suffer Ich.

Cories can get any of the fish diseases, including ich.

cories can get ich, but they dont show it the way most fish do. because of the bony plates on their bodies, you wont see the tell tale "sprinkles of salt". cories tend to get ich on their faces and their eyes are extremely vulnerable. you probably wont notice unless you cory starts to show signs of something like popeye.