Hi,
The right combination for this is:
- Filter data: Product information
- Information: Height (or Length, or Width)
- Filter type: Cursor (the slider with two handles), not Single dropdown
The cursor filter auto-detects the min and max value from your catalogue's product_height / product_length / product_width columns and lets the customer drag the two handles to narrow the range. The SQL it generates is a simple BETWEEN on the corresponding product column.
The Single dropdown filter would have worked too but it expects you to predefine the ranges manually (for example 0-10 / 10-20 / 20-30), which is why nothing showed up when you tried it: with no ranges configured, the dropdown has no options to display.
You do not need a custom field for any of this. Height, Length and Width are core columns on the product table, and the Product information filter data reads them directly. Custom fields are for adding new columns to your products that do not already exist; using them to mirror an existing core column would create a duplicate that does not auto-populate.
As a bonus, the same Product information filter also has Surface and Volume options that compute width * length and width * length * height on the fly, so you can offer those as filters too if it makes sense for your catalogue.