Now I want to invest in btc/altcoins. I'm wondering which way would be the best. Go from EUR to BTC and then to altcoin (XMR, XRP, ETH, DASH, LTC) or directly from EUR to altcoins?
It depends. The volume for the BTC/altcoin trading pairs is often higher and has more liquidity than the fiat trading pairs. Above all if you want to buy large amounts, I would go first into BTC and then to an alt.
But for values like the 350 EUR you mentioned, you can go directly from EUR into your desired altcoin if you see the price is OK - as BitcoinHodler said, you can avoid "double fees" in this cases. Sometimes you can find very good prices in trading pairs with a small volume (e.g. if someone is desperately trying to sell), but the probability is higher the price is a little bit worse because of a higher bid-ask spread (price difference between buy orders and sell orders).