Set up a search like:
~artistname ~artistname ~artistname order:id id:>0
Add in the artists you want to watch. You'll get all of their posts in the order they were posted, oldest to newest. Decide on a starting point (or just take the most recent one if you want to start from today), replace the 0 at the end with the ID of that post, and bookmark it.
When you want to check for new stuff, open the bookmark, and you'll see all posts by those artists that came after the one you took the ID from. Browse as you please, and when you get to the end, copy the ID of the most recent post, replace the ID in your search, and update the bookmark.
Also works for any search that isn't artist names, too, obviously.