I would like to make my first moves with trading altcoins. About 6 month ago I bought Bitcoins (just for fun) for a few bucks wich are now worth around 100 Bucks. I am aware that i have to pay around 20 Bucks transaction fee to transfere the BTC from my wallet to Binance.
you can choose the fee you pay. if you can't, you should use a different wallet, like electrum. you don't need to pay for immediate confirmation. right now, the cost for immediate confirmation is 650 satoshis/byte. i'm generally paying 3-4x less than that.
i can't tell from your post how many outputs you have. does your wallet just have one incoming transaction? if so, you can send all of your BTC in one transaction that is ~192 bytes. immediate confirmation costs ~0.00125 BTC in that case. i would drop the fee closer to 200 satoshis/byte, paying ~0.00038 BTC. that would probably take 5-10 hours to confirm.
But what I don't know is if this fee also applies every time I buy an altcoin with it (Besides the 0.1 % Binance fee). If yes this makes BTC unusable for trading small amounts right?
no, trades within binance are done internally. no blockchain fees (which is why they are charging you 0.1%).
So the question is: Is it smarter to use my few BTC to buy altcoins and pay ~ 20% fee or should I wait, buy ETH and then use that to buy other altcoins?
it doesn't matter. if you're holding your BTC in a wallet you control, you need to pay the BTC miner's fee to transfer it no matter what.