Software wallet is in most cases the best alternative. Using an online wallet, you do not control your coins in the same way. To buy bitcoins, you could try an exhange operating in EU like Kraken or Safello, or you could try to find someone to buy from using LocalBitcoins.
Cex.io is ok for me but it requires a selfie with my ID and photos of my ID. Is it safe?
I haven't used them myself so I cannot say for sure, but it should probably be safe. I think that all exchanges operating legally within the European Union have to require ID, so either you will have to provide it or, if you value your anonymity, buy the bitcoins directly from another person (using LocalBitcoins for example).