Can a gray card, a ColorChecker and a plain white sheet of paper all be used to PRE (Preset Manual) white balance?
No. Only the gray card can be used.
Now...having said that, I must provide clarifications. First, I'm making an assumption that you have a Nikon, as I believe only Nikon uses the term "preset manual" to describe the process of setting a custom white balance. If this is the case, then the ColorChecker won't work because with Nikon you need to fill the entire frame when setting a custom white balance. The ColorChecker patch is simply too small.
However, there are several products named ColorChecker, and the ColorChecker 18% Gray Balance, ColorChecker Grayscale, and ColorChecker White Balance will definitely work. These cards are not as durable as a plastic reference, so that something to consider. The white balance target on the ColorChecker Passport might work...but it's on the small side.
As has already been said, regular paper, such as copy paper, has optical brighteners. OBAs work by converting some UV light into visible blue light. This fools the white balance process into removing too much blue, and images take on a slight yellow color cast. Also...if you put 10 white objects side by side, you'll likely see 10 different "whites". So white is not a good tone for white balance.
That leaves the gray card. But here too there are differences between cards. Just like the 10 different whites, not all gray cards are the same "gray". What's needed for white balance is a surface that is spectrally neutral. That is...a surface that reflects all visible light equally. This is best achieved by purchasing a reference that is designed for setting white balance.
There are several on the market, such as the WhiBal and ExpoDisc. My reference of choice is the "Digital Gray Card" (DGC) by RMI. It's 4" x 6", making it a good size to keep in a back pocket, and it's a 3mm thick, plastic reference...which makes it very sturdy. It also has a very good matte surface that will reflect evenly across a range of angles. And at 15 dollars it's the least expensive of the references that are known to perform well. I have a "Digital Grey Kard" (DGK) by Digital Image Flow and that card doesn't have nearly as flat (in terms of reflectance) a surface as the DGC. The two cards are nearly identical in the WB setting you get from them, but I have to be far more careful when using the DGK because the reflection across the card isn't even. In fact, I don't use the DGK anymore since I got the DGC.
With a 4x6 card, you can hold the card right next to the lens, angled to catch the light. That will fill the frame down to 16mm/DX or 24mm/FX. Just as long as the light you're using is the same light that's falling on your subject, you'll get a good white balance.
The great thing about Nikon is that its custom white balance process is so quick and easy. Just hold down the WB button for 2 secs and the process starts. Focus lock is disabled so you don't have to mess with focus. Also, Nikon's WB process overexposes the reference by 1 stop, just to get a more accurate reading. It only takes about 7 seconds. I do it every time I step into new light.
I also use my DGC to set exposure. I have my AE-L set to "AE Lock (hold)" and my Auto Meter-off timer set to 30 minutes. This allows me to lock an exposure and take multiple images with the same exposure. So when I step into new light I'll whip the DGC from my back pocket, set a custom white balance, and press AE-L to lock exposure if the light is constant. Then card goes into the back pocket and I'm ready to shoot. Please note, however, most of these references are not sold as exposure references. In fact, RMI says that the DGC can't be used for setting exposure. This is because the card is brighter than 18% gray. But that doesn't really matter to me because even 18% gray needs +0.5 EC (as stated in the instructions that come with a Kodak gray card.) So I simply apply more compensation for the DGC. My DGC needs about +1.3 EC to get the exposure right.
Here's info on the Digital Gray Card...http://www.rmimaging.com/information/dgc.html