Hi, with classic surging in popularity again i'm going to give you a few advises on how to level in classic compared to retail. Obviously if you despise grinding and want to level up faster to enjoy that sweet endgame you can always head on to over to https://serverlist101.com where you can find a 10x exp rate server which is gonna speed up your grinding quite a bit.
There are plenty quests in retail and generally they are the best way to gear and level yourself up. Grinding mobs without doing it for a quest is pretty much unheard of, however in classic there aren't always quests for your level and even when they are they might be in a contested zone or the quest givers are simply being killed by the opposing faction. There are plenty of times when simply farming mobs can be the most efficient way to gain exp and it usually also rewards you with more gold if you pick your farming spots well.
Dungeons are a hot topic for people, but i believe that in classic dungeons aren't the best way to level. Sure they are quite efficient and if you've got a good group they can even compare to grinding out mobs on your own, however if you don't have 4 other dedicated players with yourself, you will quickly find yourself in a group of pubs and those go generally less than stellar. People simply aren't familiar with classic as much and you also have to factor in the time you're going to use to pick up a party willing to do it and also the random stops and people leaving on top of all that, all experience is going to be split five-way. The upside to dungeons is that especially after the few lower level ones, they are the best source of gear and ingredients you can sell for money, so you your gp per hour shouldn't suffer too hard on account of you leveling.
Obviously this isn't a method you can do on your own but if you can find a level 60 that's willing to take you to a few boost runs you can get to 60 pretty fast, however they will generally want compensation for that so if you don't have fat stacks in the bank this method probably isnt for you. So while this is probably the fastest method of leveling it also usually comes with a negative gp flow, taking you further away from that level 40 mount and riding skill, so keep that in mind.
In conclusion i find the best way to make money while leveling and keep up your xp rate is to supplement your questing with periods of simply farming out mobs, this will lead to you having enough money to cover your expenses and let you hit 60 in decent time. However if you're like me and detest grinding you can simply head on over to this wow private serverlist and find a server with boosted xp rate, so you wont have to waste your time simply killing the same groups of monsters for hours.