Do your homework and shop around. These aren't quick buys.
Digital pianos
Recordering devices
Not having a piano for a school thing doesn't surprise me. It's THEIR show though. Don't go too far out of your way -- certainly not spending a grand to get a portable piano quick. Shop around for that for sure. There are tons of threads on here about them. Someone else at the school WILL have a keyboard of some type they will borrow. Have the music teacher in charge of the project track one down for you.
.mp3 is a format for audio. .wav is another format. I don't know for sure what the format is for a regular CD (redbook maybe?) Does anyone know?
I'm not an audio expert. Like the pixels for pictures, dots per inch, dpi, music has its own kind of "resolution." I'm fuzzy on it exactly. There's something like "16-bit" and then the 44.1 numbers. I think the bit number refers to the size of chunks of information -- When it's digital, it's just chunks of information. The other number is the speed of the recording -- I think. It's something like that.
There is a standard bit number and other number for CD recording quality. I think it's 16 bit, 44.1. Something like that. Technology keeps improving, so you can actually get higher quality than those CD standards now -- but you won't be able to play that back on a standard CD player.
mp3 is another file format. I think it's just lower quality. Stuff is taking out of a CD quality (16-bit, 44.1 format) to make the mp3 take up less space. Less space means it's easier to pass along through the internet -- less download time. With consumer level stuff (cassette tape quality) it's not so noticeable that the quality isn't there with the mp3.
I haven't heard of any keyboard recording an mp3 directly. It wouldn't surprise me though. But then again -- You know the format will change when technology improves. I see older keyboards that required special "double high density, blah, blah" disks -- Disks that aren't made anymore.
I wouldn't get a keyboard just because it can record to mp3, esp since mp3 isn't a high quality format. If it could record straight to a standard CD.... or a standard CD, maybe CD-RW, that you could record on over and over... that might be useful.
mp3 formats can also come in different quality settings from what I understand. kilobytes per second kb/s To make it more confusing.

Samson Zoom H4 -- A lot of criticism about the difficulty of the user interface. Lots of menus to scroll through to do simple things. It can record another track though -- so you could mix and record something over your original track.
Edirol R09 -- Complaints about having to open the battery compartment to upload to the computer or change the SD card. But the user interface is supposed to be very friendly and easy to use.
Sony also has some new portable recorder out that's over a thousand dollars. Ouch.
I've heard of a lot of problems recording to a computer, straight to a hard disk. It's a computer. Audio takes up a lot of space to process and store. Problems are inevitable. But things get better all the time.
I vote for standalone recording over computers.
I have heard good things about the Alesis Masterlink and Superscope system. But that involves getting a microphone and preamp too. More shhhhtuff. More money, more complicated... but more quality then too.
"Real time" is a specific word for recording. It means the actual time passing of the recording. (Bob's brain is running down) As opposed to editting stuff with a piano roll view, or notation view -- there is no time there. Or slowing things down -- twice as slow, twice as fast. It's not the .... I can't think. (Bob gives up) Anyone have a better definition? It's either the actual regular time of the recording -- or it refers to recording or making changes in time, regular actual time as opposed to altering things on a piano roll, notation view, or with numbers -- those don't have any time.
If you've got MIDI ports on a keyboard, and the cable and interface for the computer, you still need to have some kind of software on the computer -- So the computer understands the MIDI signals coming into it. And actually -- MIDI is just information, not sound. 1's and 0's. If that's going into your computer, you record just information -- information the keyboard uses to create actual sound -- You still need the keyboard to create the actual sound even if you record MIDI information on the computer.
MIDI is information. Sound files are actual sound -- and actual sound files take up a lot more space than a little bitty MIDI file.
If you've got a headphone jack for the keyboard -- You can get a little male-to-male end stereo cord to go from the headphones OUT to the microphone IN on the computer. Then you could use Windows Recorder (some name like that, it's the little tape player in Windows, all Windows has it I think) to record. I think that Windows recorder has a 60 second limit, but I've heard there's a way around that. That will record something, but the quality may not be the highest -- It's the computer sound card that the sound goes through. There are other recorder software out there though -- free probably, I could see that. And of course there are audio recording software programs that allow editting and things. If you record that way -- keyboard to computer -- you need to crank up the keyboard volume as much as possible and get the settings on the computer set right -- to get the high volume, without frying the computer though. I think the Windows recorder makes .wav files so that's what you'd end up with. I don't know if .wav files are what a CD player uses. I know there are programs that will convert .wav files to .mp3 and other formats too I think. Free probably.
Or, if it's not a keyboard, you could just plug a microphone into the computer. But quality will probably be an issue again. If you want to play around with things, take a pair of headphones, plug those into the microphone input, adjust the volume, and record. Headphones can act as a crude microphone. But again, quality may not be the greatest.
To get to the volume controls on the computer -- If you have Windows XP, Start menu, control panel, sound speech and audio devices, sound and audio devices, in the popup window -- hit the advanced button. The "master volume" window appears. I see I have "advanced controls" checks under Options. Maybe you can get to that master volume control just through the regular volume icon. Under Options, click on Properties. Then you can decide on whether you want to adjust Playback or Recording. Check the Recording circle and you can adjust the level for the microphone -- So if you don't pick much up with a microphone (or headphone-microphones) then you can crank it up with that window. Being careful not to power it up so much you overpower things. From what I understand you are actually increasing the amount of electricity in the signal -- too much and you are "frying" the electronics with too much power, which of course damages them.