Whether the 2N2222 will be able to do the job depends on the current drawn by the relay coils. I would guess it would be no problem. There is no fundamental benefit of BJT's over MOSFET's (or vice-versa) in this application: you just need to switch the current; any transistor capable of handling the current & voltage needed to energize the coil will do.
However, make sure you install a fly-back diode over the relay coil leads, and a current-limiting resistor on the AVR output, otherwise you will fry your circuit. A coil stores magnetic energy, and switching the current off will result in a large negative voltage over the coil. Basically, the voltage will drop indefinitely until something starts conducting; if no fly-back diode is present this will be your poor transistor, and perhaps the AVR driving it.
Safety in this application is determined by:
- Ensuring through other means that even when the AVR keeps the heater on for ever, no damage will be done.
- Using a relays capable of handling the HV voltage and current with at least a 30% safety margin (preferably more: don't squibble on safety).
- Proper separation of the HV and low voltage cabling.
- Proper insulation of the HV part.
- Using cables suitable for the HV current and voltage, again with a wide safety margin.
- Using proper fuses for when there are short circuits.
- Especially the HV connections to the relays switches are important: ensure that a proper insulation distance is maintained (at least half a centimeter from any conductor for 240V). Also ensure that the wires won't detach, even when the cable is pulled!
As always, working with 240VAC can get you killed or set your house on fire! Be sure that you know what you are doing.
