I'm looking for a program to catalog my midsize photo collection (about 25K photos spanning the last decade). I'm at the point where I have so many photos that I'm starting to lose track of the context each photo was taken in, this is quite important to me so I'm looking for some software help.

These are the kind of features I'm looking for:

1) ability to maintain an index of photos searchable on tags like location, year, and custom ones like "landscapes", "to print", etc.

2) ability to batch add new photos to the index, all with the same tags/description.

3) ability to add a small description to an individual photo (ex. sunset view from Haleakala volcano, Maui) and have the photo be accessible by searching for "sunset" or "Maui"

4) catalog is transferrable between computers. I have my entire collection on Dropbox so it's synced on my laptop, desktop and my parent's desktop. I want the catalog to be available on all of these computers at best, and at the minimum I want there to be a way to easily transfer the index if I upgrade one of my computers.

What are some programs with these features? If there isn't one that meets all desired criteria, are there some that come close and what are they missing? I don't mind paying a small amount (ideally a one-time purchase rather than subscription) but obviously free is better.

One of the obvious choices is Adobe Lightroom, but I haven't found a detailed enough walkthrough of the cataloging/tagging/search/indexing features to commit to paying ~$100/year. I'm also not really interested in the batch editing capabilities of Lightroom at the moment because I have a standalone copy of Photoshop Elements that I use for <1% of the pictures. Is Lightroom still the best option?

Thanks for the advice.