I've been using SmugMug for 6+ years now and have been very satisfied. No ads, no invasive up selling, good speed, great mobile access and uploading, no security breaches. Well worth the small annual fee IMO.
FWIW - I currently have 64,199 photos on their site.
If you're interested here's a discounted sign up link:
https://secure.smugmug.com/signup?Coupon=achuJuglTx7pQ
https://www.smugmug.com/about/