What's the best thing for the future of Bitcoin the price going higher and higher (over ATH) or the price becoming stable?
The best thing would be both
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Honestly, I would rather choose the price become stable. Bitcoin price volatility is one of the main issue of mass adoption. Bitcoin's volatility is alien in other investment. You wouldn't see any stock going down by more than 10% in a day and then going back up the next day. That's crazy volatilty and it actually scares some investors out.
By stable I don't mean the price will be the same for a long period of time. Of course, there has to be some stable growth in the price as Bitcoin is a limited asset (fixed supply).