It's quite simple. Which category do you belong to?
A: I am bored with the game, but I got lots of money and want to have some fun.
B: I am quite busy with raiding and I'm trying to make some money on the side.
If you're a B, then don't bother! You'll need to spend ~1 million gold for a decent 101 toon. Depending on your server, your auction house attendance, and patience maybe half of that. If you wanna be really well equipped, then at least(!) twice of that. Up to you!
Now let's say you charge 2.5k gold for a dungeon run and you have 4 customers, then that's 10k per run. So we're talking about at least 100 runs to get back your investment of said 1 million gold. (Mind you: NOT counting the time to level the toon.)
One Dungeon takes about 10 minutes. Yes, YOU could be faster, but realistically with 4 semi-afk dudes, that's what you're looking at. Minimum! Somebody leaves, you need to search for another customer, in the mean time another one goes afk and ... 15 minutes later you and your 4 customers are ready for the next dungeon. So that's 4 dungeons per hour. Maybe 8 if things go perfect. So let's take the median of 6 runs per hour (and that is VERY optimistic) with 4 customers, paying 2.5 gold per run. 60k gold per hour! Tops!
Go anywhere! Use your Herbalism/Mining skill! Kill mobs! Loot their stuff and sell it to an NPC or on the AH. One hour of mindless farming! It won't quite net you 60k, but: No idiots to deal with! No need for trade channel spamming. No discussions about how the price, and the promised progress, and the time it took until ... blahblahblah!
Creating/playing a 101 toon is for fun! For the process of gearing up while playing the AH. For doing something different. For some interesting whispers during/after dungeons. For your Skada Epeen. For ... well ... for pretty much anything, but not for making gold ... unless you got lots(!) of time and nerves of steel.
P.S.: Choose a class that could fit any role such as Monk or Druid. Or at least one that COULD be either healer or tank. Myself, I play a 101 Elemental Shaman and when looking for a random group, I also check the healer option. That way I get instant invites and due to my gear and the kill speed, the heals are no problem at all. Kill the boss - heal the tank and some clumsy dd after the fight with just 2-3 Healing Surges.