A new quest will pop up once your first pet reaches level 3. It will send you to either Audrey Burnhep in Stormwind or Varzok in Orgrimmar. These trainers will offer a quest chain to battle specific Pet Tamer NPCs on each continent. Defeating each of these NPCs will reward a nice chunk of experience for your pets, as well a Sack of Pet Supplies (which has the chance to drop the Porcupette companion, among the always-useful pet bandages).
The leveling guides on my site are essentially speed leveling guides. My leveling guides are the same guides I use myself to speedrun to 60 on new servers to get 60 server first. I list many occasions where I tell the player to "die on purpose" to go faster. I tell the player to skip certain quests, because some quests are just not worth the time/XP. I list tricks and shortcuts to go faster so you can reach level 60 much quicker. I am still constantly going through them over and over again perfecting the guides to make them faster and easier to follow. For the most part, the guide can be followed without the need from other player's help, as the whole guide was made from a solo run anyways. Although I do list quests that can optionally be done if you have a group.
The main topic for Classic at the moment would be whether the game is actually harder or just has more redundant activities you have to do before doing the stuff that's really fun. This is actually a good discussion to have, and not just for WoW, but gaming in general. The main sticking point for now, as most people are on (relatively) low levels is the breaks between killing mobs, especially for mana users. In the beginning it's actually refreshing having to think about what you can and can't pull, not just running into a bunch of mobs and killing them in *insert current optimal time to kill Blizzard determined is the most fun*. The food/drink breaks after a few (or even one) mobs provide time to actually look around the scenery and the mobs you're facing, and while there isn't much strategy involved at these levels, you still at least pretend to plan out how you're going to get to that quest mob without being killed by the 4 random ones surrounding them. Not being able to pull whatever mob you want, and actually having to check what mobs are there when you don't have interrupts yet (casters tend to be a nightmare) is definitely more difficult in a real way than what we have today. As a caster, having to actually think about which spells to use based on mana cost (and perhaps even using lower ranked ones) is definitely more difficult and requires more engagement with your character than we have in modern WoW.