70 euro a month for gigabit? That's a great price! And way, way, way, more than you need for self hosting a website (maybe more for other things?). I've hosted my .com website from home since the late 90s and anything faster than a couple megabits is just fine .My current 80/10 megabits connection from comcast is $115/mo and has a 1.2TB data transfer cap with $10 per 50GB over. Even with such a terrible, expensive, exploitive ISP I host my dot com from home just fine.

Trying to host from wireless would probably not work so well. Do they even give you a real ipv4? And even if so, you're round trip time is inherently randomized which leads to tcp backoff and slowdowns in this context.