Unlike Classic WoW, almost every class and spec is viable in WoW Classic TBC , and some classes can perform well in raids. If you are looking for the best DPS classes for the new expansion, then you've come to the right place!
Here are DPS Rankings for classic TBC. The data is from this site, and it will be updated as the official TBC Classic releases and progresses through phases.
Hunter, Warlock, Mage, and Shaman are the top 4 in TBC DPS Rankings. Hunter, Warlock, and Restoration Shaman classes are the best of the best. They have the highest performers throughout the entire expansion. Beast Mastery Hunter and Destruction Warlock provide the greatest overall damage, while Restoration Shaman provides the best healing and top-notch utility.
In WoW Classic, the best guilds can bring a ton of Warriors to maximize damage, and that will be the same with these three classes in TBC. This is especially true for Restoration Shaman, as its healing is incredibly strong, and its Totem can provide some incredible buffs.
Here MetaGoblin will share with you the best DPS classes to play in TBC - Tier list of the best specs. Some content of this article is quoted from his video.
Hunter
Let's jump into the meat and the potatoes of this video. Hunter has very strong DPS in TBC. Many players will obviously choose a Beast Mastery Hunter, but some players will also choose a Survival Hunter. The Beast Mastery Hunter is arguably the strongest DPS in the entire expansion, and it is sure to be one of the most popular specs in TBC.
Survival Spec is very flexible. You can choose the Master Tactician Talent if you don't think you have enough crit. You can also move the points from Clever Traps into Imp Traps. You can do what you like. If you want to learn about Hunter class, you can read this article.
Warlock
Let's move on to Warlock, the second-strongest class in the game. It has a very strong and snug spot in TBC and is the second-highest DPS in single target boss fights & AoE situations throughout the entirety of TBC. A lot of players will choose Warlocks, and they will stack them in raids because the Warlocks are so ridiculously powerful that they don't need much gear.
Affliction Spec is definitely the best spec to start raiding as a Warlock. Suppression Hunter provides you with a ton of hit ratings. Affliction spec also brings three really nice buffs: Blood Pact, Shadow Embrace, and Malediction to your group! Your group member will appreciate your choice, so the Affliction spec is the best option for you.
Mage
Next is Mage. Fire Mage has a solid spot in tier 4, so most players tend to get five specs when they've got a decent amount of crit gear. They can get Ignite and do really good damage. Ignite also touches off 
Meteor if the Mage is talented into this spell.
When TBC launches, many players will jump into TBC with tier 3 gear, so they probably will have a lot of hit chances and crit chances. Arcane is an interesting choice for Mages. It requires mana management but provides you with great burst damage. If you want to dabble in Arcane Spec and Frost Spec, you probably won't see them very often. When you get a particular set bonus that increases the damage of Arcane Blast, Arcane spec will become really solid again in tier 5. Frost spec is slightly worse than Fire spec and Arcane spec, but it's also very useful in dungeons.
Shaman
Let's move on to Shaman. Restoration Shaman is a versatile healer, and it is well suited for any situation with numerous passive abilities by reducing the casting time and mana cost of healing spell while increasing its effectiveness. On top of that, it offers good utility (like mana regeneration uses 
Mana Tide Totem) and strong multi-target healing through 
Chain Heal and 
Healing Rain. Signature abilities include 
Earth Shield, 
Riptide, a long-term buff, an instant cast heal, and an HoT.
Elemental Shaman is a very snug spot in tier A. It is a utility damage class. It can heal a limited emergency situation with DPS gear. It can also provide a non-healer resurrection option to reduce healer downtime on raid trash.
Rogue
If you want to succeed in raiding as a Rogue, you should do the following DPS optimizations.
1. Don't die.
2. Don't do anything that risks wiping the raid.
3. Maximize your time on target.
4. Don't let your energy cap out.
5. Use one of the spreadsheets to figure out your best cycle.
6. Use your cooldowns.
Warrior
Now let's move on to Warrior. The Warrior moves around the tiers depending on what phase of the game you are playing and what content you are clearing. When Warriors start to get more and more gear, they will start to pump up more and more damage, so they're fair enough to start in TBC.
Priest
You have the ability to heal yourself & your group member as a Holy Priest, or you have the ability to do damage as a Shadow Priest. It gets a good spot in tier B, but it is not the best DPS in the game. It provides an immense amount of support for the entire raid. Actually, it is in high demand, although it is a tab class. Every raid needs at least two shutter Priests. Ranks in Improved Mind Blast and Shadow Weaving can be changed depending on your performance.
Druid
Feral Druid is a snug spot in the tier. It also provides immense map support for the raid, so it is a strong class to own, and it can very quickly and easily swap between tanking and DPS, which is very useful for raiding.
Paladin
Compared to WoW Classic, Retribution Paladin will get a lot of improvements in several areas that make it more competitive with other classes in TBC. The most impactful of these improvements is Crusader Strike.
It has a snug spot in tier B, and it is a strong support class in Raffle Lich King. Retribution Paladin isn't the top meter to support the raid with everything that you bring to a raid, and your spot is more than justified. You will do slightly less DPS with this class.
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