Need help with selecting an antenna for PCB
The big question is: what distance do you want to cover? The data sheet of the transmitter quotes a maximum range of 50 metres [about 150 ft]. Will you use that, or will the receiver be closer?

Any oscillating signal will radiate: the whole point of the USA's FCC is to limit the amount of annoying [or dangerous] EM radiation coming from devices. Depending on the range, and the presence of bulky metallic objects between transmit and receive, Your Mileage May Vary.

Antenna theory and design can be taught in depth by amateur radio enthusiasts, or groups like ARRL. For starters, a simple piece of wire about 20cm long can act like a "whip" antenna: keep it clear of grounded cases, and it should be enough to get you started. A second piece the same length can act as your receive antenna. Start with the circuits next to each other, make sure they work, then seperate them. If they stop working before reaching the seperation you want, THEN [and only then!] consider delving into antenna theory...

If you need more, I'd suggest TI's Application Note #AN058: http://www.ti.com/lit/an/swra161b/swra161b.pdf

And: http://www.picaxe.orconhosting.net.nz/yagi433.jpg