OP can start with these two news groups on telegram: @coinnewschannel and @cointelegraph. I started with them as a newbie and they were really fantastic. Later you can branch off to news sites on Twitter.
If cointelegraph's website isn't even good then why do you think their telegram group would any be better? I took a look at it and my guess was right it was only their channel to promote links of their news article. It's even worst for coinnewschannel's TG group as aside from news links they also have links from airdrops and other promotions which isn't a goo idea. OP would only be wasting his time here with their Clickbaity articles. I'll still go to r/Bitcoin or r/Cryptocurrency in Reddit to get my news, at least they provide direct links from media sources not related to crypto news directly.
I agree with Theb lot of news sites are promoting crap , but not concentrating on real news
Still can't understand what's wrong with cointelegraph, to my mind they are amazing and I personally like news they publish, they publish news asap from my experience, I usually read BC news.
OP I highly doubt any website will publish articles faster then cointelegraph, ccn and coindesk.
Like user above your post mentioned, reddit is a great place for what you need.