Creating picture database, how to and what to use?

Definitely Access - I have moved the thread accordingly.

MS Access, MS SQL Express, MySQL.
Any of these can do the job.
While it is possible to build using Excel... anything beyond very rudimentary data store (along with path/link to image) is going to be more work than what it's worth.

But you'll need to evaluate best fit solution based on your need and what tools you pick as front-end.

For an example, if you want to make this db/tool available outside of internal network (i.e. accessible from public network).
You will need to go with MySQL or SQL Server (not Express) + web application (ASP .NET, php, etc) to serve as front-end.

There are many open source software/cheap software out there that may serve your need better.

Ex:
OpenKM - Open source document management system
SharePoint - If you have Enterprise SKU for Office 365 you may already have this. SharePoint uses MS SQL Server as backend and has robust search algorithm along with document store and workflow.

No server agent and can't use jobs I've had to deal with this at my work. While there are workarounds it's not ideal.

If they're considering access though, I'd say that agent jobs will be pretty far down the list of requirements!

Ah, true.

As a side note, if you add linked server, you'd want server agent as well.
Otherwise, it's going to be a headache, as SQL service will stop any time there's issue with query to linked server. :p