Power requirements for NFC (RFID) chip
If you read the datasheet, it gives information on the typical and maximum current consumption for the IC. It also gives power down consumption and other details. I'd also check the other documentation (app notes, etc) to see if there is more information/advice on power characteristics.

On page 3 note 7, it says typical current consumption is below 100mA. 60mA is given as the typical consumption for the transmitter supply, digital and analog ~7mA each, and the pin supply up to 40mA. With this info you can get a pretty good idea of what capacity battery you need for 10 hours operation.

Assuming maximum consumption, and less than 100% efficiency (e.g. regulator used) we can do some calculations. We'll assume 80% efficiency and 100mA continuous draw:

100mA * 10h * (1/0.8) = 1250mAh

This is probably very, very conservative, but gives you a figure which will certainly be plenty. However the only way to get very accurate figures is to run some tests yourself, since consumption will depend on how many IO pins you are using, other circuit activity, regulator efficiency, temperature, etc, etc.   

I would probably look at using a 3.7V Li-Ion cell, since it's a good voltage, they are conveniently sized and there are plenty of options around 1000mAh (eBay, Sparkfun, Digikey, etc) There are also cheap charging ICs available (Microchip do some good ones) Of course it's up to you, anything that provides the required capacity would work, but you have to consider what is most suitable for your project (size, weight, cost, etc)