I don't know when was the last time you tried to level, but if it was before Cataclysm, then I think you will have a much easier time this time. The quests are far more streamlined and user-friendly, and the xp is scaled such that, if you go for 100% quest completion in each zone, your quest log is likely to start turning green before you finish the zone, depending on how much rested xp you have and whether you are using heirloom gear. But in the end what will get you to the max level is keeping it fun. While it's true that some times a grueling experience ends up feeling very rewarding when you look back on it, this is a game and it sounds like you're not going to get very far just by pressing yourself. So just take your time and take time to enjoy the content, instead of staring at your xp bar, willing it to move. Some of the questlines in the revamped classic zones are really cool, and are a genuine pleasure to work through, so take the time to read quest text to follow the story. Personally, my favorite zones are: Westfall (A), Redridge (A), Duskwood (A), Hillsbrad Foothills (H), WPL (both factions have quests, but I like the Horde version better), Badlands (A/H), and Winterspring (A/H). The two best quest-chains in the game are in Westfall and Badlands. Badlands is also home to the famous "The Day Deathwing Came" mini quest-line, which is a must-see for everyone, and is open to both Alliance and Horde.
As for PvE or PvP, I think if you have any doubt, you should go with PvE. The PvP rule-set caters to a very specific type of player that does not really get along with other types of players. PvP servers are also going to be tougher on beginners, because getting interrupted in what you're doing by having to make corpse runs can be very frustrating and discouraging.
Now, pets is a very personal thing. All pets are viable for solo-leveling, but each family does have it's own perks and I really think which family is best for you is something only you can decide with experience. As far as I remember, all hunter races start with a Ferocity pet, which is the most DPS, so that will be a good starting point. You can only have 1 pet with you for the first few levels, and you can't tame pets until level 10, so that will give you some time to get acquainted with your starter pet and see how you like it. In the meanwhile, you can browse the Petopia pet gallery and see if there's a pet that looks cool or sounds like it has a neat ability (I was pretty big into Dragonhawks for a while because of the Fire Breath ability
), and make your plan to go tame one. In more objective terms, Cats will make the most "useful" pets because they buff your Agility, which translates to more DPS for you, and they're a Ferocity family, which means they will help you kill things a bit faster. I also love the self-heal that is deep in the Ferocity tree (Lick Your Wounds), which could come in really handy if you accidentally pull too much or are trying to solo an elite. On the other hand, Turtles are also nice because they have the Shell ability, which reduces their damage taken by 50%, so they can take more of a beating, and Tenacity family pets have Thunderstomp in their tree, which helps them maintain aggro against multiple targets. But again, I must emphasize that what pets would be a good match for you is a very personal thing and likely to be completely subjective, so just keep an open mind and keep checking out pets and playing with them
I don't think you have to worry about gear too much. If you can get BoA gear, that's great. If not, quest rewards will keep you suitably clothed pretty much the whole way. The biggest jump you'll have to make is from Northrend to Cataclysm zones. If you're only wearing Icecrown/Storm Peaks quest rewards, prepare to take a long time to finish the first round of quests in Hyjal
Of course, at that point, you can probably grab some green Cata BoEs from the AH for fairly cheap, but I would say this is the only point at which buying gear off the AH is worth it (until you start trying to do heroic dungeons and need better gear).
If you're set on Horde-side and Beast Mastery, Orc would probably be the "best" choice in terms of racial bonuses, because they have 5% increased pet damage, and Blood Fury is also a good DPS cooldown. But if you're not max/min-ing for endgame, just choose whatever you like. Again, this is a personal choice. I personally like Blood Elves cuz they're pretty