Likely you can do it for free.
I did a similar project some years ago using Microsoft Access database.
The term "database" tends to overwhelm some people but with the wizards that are now available you can create a simple database very easily.
If the data is already somewhat available via a spreadsheet for example you can either link to the spreadsheet or import the data.
Key is having a field in each record that contains a link to a picture of the painting.
And you do not necessarily need to use Access. There are free database apps readily available.
Do a couple of trial runs with a representative sample of the paintings. Put the necessary data into a protected (Read only) spreadsheet and import the data as applicable to each database. Saves retyping the data.
Consider using a barcode for each painting - you can easily get or even print out your own barcode lables.
One record being, for example:
Barcode (Key)
Artist
Category
Date
Location
Image (photograph of picture)
Notes
Etc..
There are some rules and practices regarding good database design. However, those can be deferred to some extent with respect to just a pilot or test database.
For example paintings may be stored in different locations: E.g., Basement, Main Gallery, Attic, Off-site, On-loan. You would use a location key to facilitate tracking where paintings are stored and the ability to add, change, and delete locations.
That gets into database design and "normalization". The latter, when seriously applied can get quite technical. However, if you google for a few database design tutorials, you will most likely get a good working grasp of what is needed for your inventory requirements.
Another thought: Consider looking for inventory tracking software. May be some canned app directly suitable for your requirements.
Google "inventory database free". Revise the search criteria as necessary thereafter. Lots of options.