12v Relay with arduino

Hello!

I want to operate -> http://www.ebay.com/itm/110766314224?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1439.l2649#ht_3336wt_1187
These with a Digital output from an arduino mini. Im pretty sure i need transistors to activate the relay.
What kind of transistors is suitable for activating the relay? Also on some of the relay shields ive seen there's a capacitor. What is the function of a capacitor in this circuit?

Why that relay specifically? It's got a 12V coil so you will need to give the driver circuit its own power supply as well as amplifying the Arduino output through a transistor to get enough current to operate it. If you're switching mains voltage, you'll obviously have the high voltage hazards to deal with. There are standard relay plugs that will take that sort of current up to main voltages, but I notice they carefully avoid saying it's safe to use them like that - because, unless you know what you're doing, it isn't.

Listing of 5V coil relays rated at 10 amps.

The relays are switching current from a 12v battery, and ive only worked with 12/24v relays. never occured to me that i could get 5v relays.
If i use the 5v relays, should i still use a transistor to power the coil? If so what kind?
http://www.ebay.com/itm/20pcs-PCB-Relay-Coil-5V-DC-Contact-1A-/190400246566?pt=LH_DefaultDomain_0&hash=item2c54bd3326#ht_409wt_833 Thinking of buying these instead then.

Still curious to why the cap is present.

-Thomas

seriously, $22 for a 5 volt relay? Check the link I provided. Grab a 250VAC/30VDC relay with a 5 volt coil, stick a diode across the coil, and be done for under $1.50.