Are you willing to pick a content item dynamically or will it work if you pass that from config settings?

Can you also give a highlevel idea of what you want to acheive, so there may be other implementation approach that you can try?

Preferrable is of course that you can pick it dynamicly like a normal content selector.

What I want to do is to search for specific products and variants but I waat the user to be able to select a specific category to search within. 
I have solved it by rendering the catalog tree in a dropdown, it does the job but of course a regular content picker would have been better.

In that case, following link may help in rendering the content picker

https://blog.mathiaskunto.com/2012/07/14/how-to-open-those-episerver-edit-mode-selector-browser-popups-in-your-custom-properties/

This will help :)

Yes, that helped and was really useful. But there was no way to get a dialog containing the catalog tree, just the page tree.
Dates worked just fine so I guess I will just use that.

The dialog I'm looking for is the one shown when adding a category to a catalog content in the Commerce GUI or adding the catalog in the asset pane.
I also tried to add the catalog as an Id to the dialog:

/episerver/CMS/edit/pagebrowser.aspx?id=-2147483629__CatalogContent

But that threw an exception.

For that I will need to do little RnD. 

Did you tried passing ID with this url? (below)

/secure/ui/CMS/edit/pagebrowser.aspx

Both: 

/secure/ui/CMS/edit/pagebrowser.aspx

and 

/episerver/secure/ui/CMS/edit/pagebrowser.aspx

Gives me a 404