So I was pretty set on having Tailoring/Ench for nice gear while leveling but now I'm considering taking Engi/Mining for all the different little things they can do.

What do you reckon is better? or should I take different professions entirely?

If you want to have more potential in pvp, get engi mining and when you get enough mining mats, change mining to enchanting. It will be expensive but it might be worth it.

I was mainly thinking for leveling and just playing in general, I might pvp a bit but I won't be pushing for rank 13

It sounds like good emersion to have engi on Gnome but it depends on what experience you wanna have, what are your goals.

Honestly im not too sure what my goals are. I know I want to get dungeon set 1 and 2 just because and id like to raid a bit as well

If you dont care about maximizing your gold income then Engi/Mining is fine. Engineering is quite a gold sink and you wont make much money from it. You can make decent money of mining though. Engi is good for maximizing your dps in raids, provides additional cc and dmg for pvp and brings a lot of flavourful gadgets which can add a lot of fun to your experience.

With Tailoring you can make bags, levelling gear, bloodvine set (which comes in ZG patch and is bis for long time) and other stuff.

Enchanting can be very profitable once you get some nice recipes which might be kinda hard to get. I personally dont have much experience with Enchanting so I will leave it to someone else.

There are very few situations where people can make a strong argument against Engi. Almost every class/spec in both PvE and PvP will get immense value from engi. It truly is the master profession. It is incredibly imbalanced and overpowered. That being said, you will likely have certain obligations depending on your guild or your gear that require you to take other professions. You may be the guild enchanter for example, or you may find yourself getting an early flask recipe and opting to go alchemy... Outside of these outlier situations, most min/maxers will eventually find themselves blending two finishing professions because the value of engi is simply too high to pass up.

Don't be afraid to change your professions several times throughout vanilla, it is very quick to level up new professions once you are at max level. Engineering for example, is relatively cheap to level up and can be done while sitting in a major city. Focus on leveling with skinning to supplement your leveling costs. Take something that will stabilize your economy and help bloom your income into a quick epic mount at 60 and then reroll later to maximize the throughput on your character.