I find it slightly annoying that on the "What you will need" page it says "some" resistors and "some" LEDs. How many is "some"? Two? Twenty? Four thousand eight hundred and twenty seven?
As for the resistors, they're being used to control the current through the LEDs. Almost certainly the LED won't die if you give it 10% extra, and won't be very much dimmer if you give it 10% less, so 1% resistors is over-kill, as pcmanbob suggests.
220Ω is one of those preferred values, so more easily obtained than, say 210Ω, so that's probably why it's suggested.
Power-wise, the voltage across the resistor will be in the region of 3½v (5v less the LED voltage) so the power dissipated will be about 56mW (3.5*3.5/220 W). So ¼W (250mW) will be fine, or you could use ⅛W ones
However, I've found in the past that the leads on smaller-power resistors won't fit snuggly into those female-female jumper leads, so don't go too small!
http://cpc.farnell.com/search?ost=220%c ... nce=220ohm
A pack of 100 5% ¼W from CPC will cost you 57p. 1% ones are 72p for 50 - almost three times the price! Don't waste your money!