Within the context of Classic, the method most frequently proposed is to re-tune bosses to make them harder. Rather than copying the numbers, re-create the relative difficulty. Kind of like, when you first start working out, you use small weights. When you get stronger, you lift bigger weights. The WoW community is more knowledgeable, more experienced, has better hardware, etc. We're "stronger." So give us tougher bosses. There are a lot of forms that could take. Bosses were constantly re-tuned during vanilla anyway, so if Ragnaros does 10% more damage or something, is that really a problem? I don't think it is. What about resistance gear? back in the day, collecting resist gear was a thing people did. But the numbers and strategies are so well known today that only the tank really needs it anymore. Bosses could be re-tuned with more resistible elemental damage so that's important for entire raids to gear appropriately. That would be entirely keeping with the spirit of vanilla even if the actually numbers sitting in a database somewhere were different than they were ~13 years ago. If you want to go a little farther, a few people have proposed adding new abilities to old bosses, adjusting their timing, etc.
I recreated my very first character -- a human warrior, because in the last-push alpha test I joined in 2004, there was no Horde -- and logged in. Immediately, I was surprised by how good the graphics actually looked, for being 15 year old textures-on-polygons. Warcraft's bright colors and cartoony aesthetic continue to this day, so all the increased resolution and better-contoured characters in Lordaeron don't really change the game's visual aesthetic.
When hovering over an ability, the tooltip will tell you whether or not that attack is weak or strong against certain pet types. Additionally, you can hover over the opposing team's pets and view their attacks during combat. This will be important since it’s a good idea to pit a pet that's strong against the opponent's pet who's vulnerable to that type.
I have tried it a few times. It's good if you're new to the game. Otherwise not so much. I found I leveled slower by using it, as it's suggesting to take the longest possible route usually. Basically following roads everytime, when you could take an easy shortcut. Especially if the shortcut involves a bit of fall damage, it's out of question. The "go here" spots don't also update if you take a shortcut, and then the waypoint arrow points to wrong direction. But perhaps it has been updated since then.
Different qualities aren't limited only to wild pets—many rare World drops and special non-wild companions have had their stats boosted. For example, the world-drop dragon whelps (Azure Whelpling, Crimson Whelpling, Dark Whelpling, and Emerald Whelpling) are of [rare] quality. Check your Pet Journal to see the color-coded rarity of your non-wild pets.
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).