A higher rated relay may need higher current to operate but will have better internal contacts to use higher output current
I haven't used either of those relays, but, in my experience, the 5th pin will be normally 'ON' and when it switches, different pin becomes on and the ON pin will be OFF
Do you have circuit diagram of pin out?
Using a 12 volt relay in a 5 volt system and not knowing the difference says you probably don't need to do this as a first project. Personally I would not do it at all like the instructable does because he doesn't even insulate mains voltage on proto board in a water involved situation. What if the pump leaks and water gets to mains and shorts out causing a fire.
OK, I just looked through the entire Instructable, you will need a 5 v relay or use something to switch on a 12v relay (Transistor or Mosfet?)
The Instructable isn't too complicated for a first time project in my opinion but I would use some form of ground/short circuit protection particularly if your in USA as wall outlets rarely have ground fault interrupt (GFI sockets ) outside bathroom and kitchen (not even then if older construction)
You could use a double socket and 12v 'wall wart' instead of 9v battery to power relay and Arduino
I get a feeling that you may want to "refine" the project a little. Yes, run it from an external power supply if you can. Alternatively (and even as well as) look at low power operation. You don't need to be sampling the soil 10 times a second - why not sleep for an hour, then sample it once, and only if it is below your threshold do you then need to worry about more frequent sampling. Also that would help reduce electrolysis of your soil probes (and needless aggravation to your worms).
Even better, replace that probe with a capacitative one that wouldn't suffer from those kind of problems...