I'm from Germany and am using Consorsbank which is owned by BNP Paribas. BNP Paribas is a French bank that falls into the "too big to fail" category. For trading shares the broker doesn't matter much anyway since the shares are in your name. You can also look for index funds but you likely want "Indexzertifikate" without the additional management fee. The problem with certificates is that they are only as safe as the issuing institution. Its just a fancy form of an IOU and if the bank goes under it takes your money with it. So you may want to look for a bank that will not go under. You are in Germany so Deutsche Bank seems like a good choice. Have a look at the DB X-Trackers certificates from "Deutsche Asset and Wealth Management" a subsidiary of Deutsche Bank. You can purchase them via your prefered online broker. But the broker will never recommend them to you since there is not much money to gain from recommending them. No bank will ever recommend them either they will try to push their own products that bring them a hefty management fee.

I personally will not buy anything that is a certificate since i frankly don't trust banks. I'm pretty sure even Deutsche Bank will find a way to let their subsidiary sink if it threatens to take them down with it...

You can also go to your local "Sparkasse" they also offer online broker services. I don't like them. They are expensive and unflexible. Often they will cite you in for minor reasons just to push their "products" on you. Most of their products are bullshit ("Prämiensparen", "Bausparen").. My local "Sparkasse" was the only institution that i ever experienced having shop opening times for a webpage (no transaction at night).