Resizing pictures for WordPress

I’ve really been struggling, trying to resize my artwork so it’ll show up decently on my blog. Although they loaded fine and looked great on my computer, they loaded very slowly and looked bad on the computers at my workplace. So last night I went through my Photoshop art and resized all of it, generally to a 1000pixel resolution. The result: they look pixellated now, very bad. Here’s the link to my site: https://www.toonicornstudio.com/

The odd thing is, I have a DeviantArt.com account and I’ve had no issues whatsoever loading my art on that site. I just convert my TIFFs to JPEGs and download the JPEGs to DeviantArt and viola! The art loads quickly on ALL computers I’ve tried and it looks great. Just what the HECK is the issue, then, with WordPress? I’m getting very frustrated. How small should I make my art before loading it onto my site? I use Photoshop for converting, if that helps. If someone could give me some idea as to the best size overall for my JPEGs, that would really help.