[Heavydrop]

In my experience it depends on the scenario and your preference, and even sometimes the availability of which pet you have.
Earth pet is useable for tanking and using its root to split spawns and keep runners from getting friends as they flee but they are at the low end for DPS. If I am in a group I don't use them unless nobody else can root, and that is very rare. I've used earth pets for farming and some exping but not that often.

Water and Fire are much better DPS and if you're going to solo Fire is where its at.
You can either heal your pet as you go (the last pet heal spell we get is level 20, and the amount we do goes up as wel level) or you can "chain pet" as is the custom of some mages.
This eliminates the need to waste all your mana healing up your pet and also cancels out the 50% exp penalty for our pets if they do over half the damage to a mob (but remember damage shields are neutral damage and don't count towards that)
Air pets are ok but their stuns aren't anything that great I've noticed until you get the level 53 air pet which is a beast.

When you get to the level you can start summoning Swords of Runes make sure to give them to your pet because they will proc on anything and do all the Temple of Ro pet focus items (I did) you never know when you're going to want a certain pet.
I prefer to group but of course I've had to do my fair share of soloing.