Best Conceal and Carry Caliber?

There is no "best" caliber as there are too many variables involved. Picking a carry gun should be decided more on how much concealment is necessary and the ability to use the gun proficiently than caliber. If it requires a bit of work and concentration to hit on the range, it is likely you will do much worse in the pressure cooker of real life. I use one of several guns for carry depending on the situation. When it gets cold enough to require a jacket, I carry a Springield Ultra Carry in 45 ACP as the heavier clothes provide plenty of concealment for a largish gun. It was also my duty gun for a few years so I was very familiar with it. For summer and semi dressy occasions I'll carry a .40 S&W Kel-Tec P-40 as it is a much smaller gun which is easier to conceal. I'll also carry this gun in an ankle or vest holster as a back up gun (BUG) when working. I recently bought a Springfield XD-40 compact which may become my main CC gun as it works the same as my duty guns; I have occasionally found myself forgetting to release the thumb safety on my Ultra Carry when practicing. I sometimes carry either of my present two duty guns, a 4" Service Springfield XD-40 and a 5" Tactical XD-40 but they are a bit longer in the grip which makes concealed carry a bit harder if using inside the waistband (IWB). I recently bought an XD-45 Service model but it too is a bit big for regular concealment usage in my opinion as the grip is even longer than on the .40s. For a number of years I carried an S&W M-66 in 357 mag for both duty and off duty use but a mid to full size revolver can be uncomfortable to carry at times.
I've carried everything from a .380 ACP up to a .45 ACP and feel that anything from 9mm on up with decent bullets will work fine for carry use. I pick 9mm at the minium as there are a number of guns for this cartridge that are as small as the vast majority of .380s so see no real need for the smaller cartridge. Pick the gun that you feel comfortable with that meets your carry needs, stoke it with quality ammunition, practice regularly, and you should be fine.

Smith & Wesson 340PD ultra light .357 magnum, add laser grips and you got a sweet package

Uglydog, as usual, has given terrific advice. The only thing he got
wrong was his name of Uglydog. He should have called himself
smartdog. I am sure it would be more accurate. To reiterate some
of what he said, you can use many calibers to get the job done.
This is because many calibers will do the job. Many subtle things
come into what you choose for conceal carry. It should be comfortable
and it should be up to the job. This is not rocket science. Take
these tidbits of knowledge and pick something. Learn to use
it well and make sure it works all the time, everytime. Practice
enough that it is second nature whenever you use it. Pay
attention to the advice like, "forgetting to take the safety off".
Another reason to practice. Practice like you actually will
have to shoot. If it has a safety, then start with the safety off
everytime you put it into action. Don't put the safety off at the
start of practice, and leave it off for the next 100 rounds. I would
really suggest a conceal carry gun without a manual safety.
In this day and age, why not make the safety part of the trigger
mechanism? That being said, if you really know your gun, it
doesn't matter that much how it works. Practice, practice, practice.

I don't have my CCW (yet), and I'm not any kind of law enforcement (yet), but from my years of shooting and using the weapon between my ears, I've come up with some thoughts on what I would carry. It would have to be a hammerless .38 snubby, hands down. Like I said, it's what I would carry. Something else may fit your intended useage a bit better. Carry what you shoot well.

Reasoning for my choice:
Yes, I love my 5" 1911's almost to the point of obsession, and I love my medium frame .357s even more. I will most likely be buried with my 4" GP100 on my hip. There are many guns out there that I would certainly trust with my life. Having said that, if I had the option of carrying something in a holster on my belt out in the woods as an "insurance policy" against whatever might get pissed at me, the bigger guns with bigger bullets would win hands down. However, we're talking about carrying concealed for the sole purpose of defending ourselves against (most likely) two-legged predators. This dictates something small, light, and.... well..... concealable. If you go by statistics (and a little common sense), things will most likely be fast and be over very quickly. You need speed and simplicity to go with your concealability. It's hard to get more simple than a DAO revolver. It's the original point and click interface. That, and 5-6 rounds is something I'd be plenty comfortable with.
Accuracy isn't going to be too much of a worry, since you're more than likely going to be damn near waltzing with your opponent when your boogerhook pulls the bangswitch anyway. Shorter, concealable barrels win here.
Then it just comes down to ammo. .38Spl, when loaded with good defensive bullets, especially in a +P cartridge, will be sufficient. No, it doesn't have the "one shot stop percentage" of a .45ACP HP or a .357 mag HP, but it's still high, and I'd be pumping every shot I had into the guy anyway. It's a hot 9mm HP being fired out of a revolver, basically. Unless they're in body armor, it will do the job if you do yours. It kicks in a lightweight snubby, but it can be controlled, especially if you put good grips on it. I wouldn't bother with .357 mag in one. You need 4" of barrel to get the magnum performance, and it'll hurt you as much as it hurts him with such a lightweight piece.

There you have it.