I manage two private art collections and both use ArtBase.
They have a product that is designed specifically for private art collectors.
I have been working on ArtBase for the last ten years and they have stayed current with technology. They now even have a mobile app. You can attach images, documents (word, excel or pdf formats) right in the database. There is a module for tracking financials as well as conservation, loans/exhibitions, provenance, location history, framing & crating, artist research, separate notes and description fields as well as a rolodex. It also has report writing features (both canned and custom).
I have experience using The Museum System, ArtSystems, a custom Filemaker database, and a custom Microsoft access database and ArtBase has been my favorite thus far. It is very intuitive and has everything that you need and more.
I have also heard good things about Collector Systems but have not had the occasion to test them out.
I hope this helps.