Specialized bike store or general sports shop
I'm not sure about Austria, but here in the UK many general sports shops are no more than outlets for Nike and Adidas clothing. If you are someone who knows very little about bikes, I'd suggest that this would be riskier than going to a specialised bike shop.

The only thing that would possibly make the general sports shop more attractive would be price. But you live in a capital city, so surely there are enough outlets to keep prices competitive?

So I would say that if prices are similar between general shops and bike shops, then its a no-brainer to pick the bike shop because they'll (likely) have a higher level of expertise, in terms of listening to your requirements and proposing a suitable bike. People also place value in building a relationship with their lbs - this may or may not be important to you, but certainly it can't harm.

If you are tempted to go to a general store, for price or any other reason, maybe you should at least apply some due diligence. What should you do if there's an aftersale problem? What do they offer when its time for a service? for example. Some "general sports shops" (such as Decathlon, do you have them?) will also have in-store bike mechanics, which would at the very least give you some confidence that they are able to maintain what they sell.