The wife and I are using Uniden SC230 scanners. These scanners are not the cheapest thing you can find, but they have the most channels and dynamic memory operation, which allows them to be used at multiple races. Most everyone prefers scanners with at least 200 channels so that the channel number can match the car number, ex: channel #8 = Dale Jr frequencies for the cup race, #108 = Busch car. Think about going to a Busch and Cup race on the same weekend...you would need at least 200 channels for that to work. Add a 3-race weekend with Craftsman trucks or IROC and you need a scanner with more than 200 channels. The SC230 scanners have a nice small size, convenient to carry, work well, and can allocate 1600-2500 channels AND ALLOW ALL OF THEM TO MATCH THE CAR NUMBER DIRECTLY, you won't even have to put them in banks of 100, 200, etc. I always add a car number for the PRN radio broadcast plus a channel (car no) for the TV frequency set.
These scanners come pre-loaded with racing frequencies but the way they are loaded is terribly confusing. You can have any of the scanner companies reload (reprogram) the scanner channels at the track just before the race for $5, which is what I did last year. I started programming it myself this year but honestly I waste at least a couple hours setting it up. For $5 it's a deal just to have it reloaded with current frequencies at the track the day of the race.
I have run 2 headsets off of 1 scanner several times, but I'm not sure one scanner of any brand/model will power three different headsets well. You can get a 1-into-3 amplifier from Racing Electronics which should solve that problem.
I bought my SC230s on ebay, but that option probably doesn't get them to you fast enough for your race. You can buy them from race-oriented dealers at the track's merchandise trailer area (or off their websites) for just a few bucks more than I paid on ebay, and they will usually cut you a deal on a full setup with headphones, your 1-into-3 amplifier, etc. Take a look at the prices on racingelectronics.com, racescanners.com, racescan.com, trackscan.com, etc.
Be sure to get 25db noise reduction headphones, which price about $60 per set. Anything less and they won't block the race noise enough. These are aircraft-quality headphones and protect your hearing from damage, and allow you to listen to driver channels or the radio broadcast without turning the volume up too high. You won't need ear plugs or any other type of protection if you get the good headsets.