I'm in the same boat and need to upgrade both Mavericks and Photo Management.
After a bit of research, here's what I've decided:
1. Adobe Photoshop Elements with Bridge offers a great basic system that's likely to be around for a long time.
2. A better product is Luminar2018, but their photo management (DAM) component will be added (free) in June 2018. Great reviews , good price, can use on up to 5 of your computers.
3 If you were to add anything else, consider DxO Photolab. Some nice features to bring out the best in your photos.
I'm opting for 2 and 3.
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