Lightroom is great at organization and tagging, once you get over the pain of understanding how a catalog works. The LR plugin makes Smugmug so nice, there’s one for Zenfolio as well.
If you go the Smugmug route we have a 15% discount for the first year. If you don’t need to sell prints directly it’s one of the cheaper options.
The search works very well on Smugmug, Zen works fine too, both search keywords, although I had to turn off my ad blocker for the zen search to work. You’ll be happy with either, just my opinion but I feel Smugmug is light years better. Best best is to do a free trial with both and see which one you like better.
Keywords you enter in Bridge will carry over to either platform, this is just saved in the metadata of the file, it’s certainly not necessary to use Lightroom.