Since it is not affected by anything i have unlocked (through levels, raids, card packs, ...), is there anything that gives me an advantage for the arena-mode?
Game knowledge is very important in Arena, to play effectively you need to be familiar with the class you're playing and all the cards in the game. There is a large component of luck in Arena, both in the draft and in the actual games, but there is also a significant skill component.
The actual games are similar to the other modes, with the exception that you can't rely on the two cards per deck limit to guess which cards your opponent might have on hand. The decks are also very different compared to constructed and rely much more on strong individual cards than specific combos. But most of your skill from constructed play should transfer to Arena.
Drafting is the most difficult part for a new player, I'd strongly recommend to use a drafting guide like Trump's Arena Tier List to help until you're comfortable with it.
If you enjoy the Arena mode more than constructed play, just start playing it and don't worry. If you don't enjoy it, just ignore it. If you're good enough to get more than 4 wins regularly, Arena is also more efficient than buying packs.
In short, I'd recommend to play Arena once you feel reasonably comfortable with the general rules and tactics. If you win less than 3 times on average you might want to practice a bit more before playing more Arena. Then you're likely making too many mistakes in either drafting or playing.
There is nothing you can do give yourself an advantage when it comes to arena. Everyone has to choose 1 of 3 randomly generated cards from the entire deck list (apart from promotional cards e.g. ETC and Gelbin) 30 times. The rarer the card, the rarer it is for it to show up in the arena. You may argue that someone gets lucky by getting one or more legendaries and has the advantage, but drafting a successful arena deck is mainly based off of card knowledge and knowing what card to pick in which situation e.g. picking more low cost cards if you have too many high cost ones or not picking a card heavily reliant on synergy when your current deck cannot take advantage of it.
Knowing a tier list can be quite important when you are just starting out. Many cards sound good on paper but can be outmatched by more basic cards. It is best to go for a safe draft when picking for arena; as the cards you can get are random, you won't want to be betting on getting a certain kind of card to enable synergy e.g. picking a lot of spell damage minions when you have no spells.
As for when you should start paying arena, well it all depends on your skill at both playing matches and drafting a deck. You may want to focus more on constructed play until you are comfortable with creating a good deck and have decent knowledge of most or all cards. I would suggest visiting the arena ever so often and see how you finish most times. If your wins are high you can safely do it more often, if not then I would practise more.
You need to be good before you enter arena
You need 3 wins to make it better then just buying packs but if you can get a good run you can get close to 1000 gold for it