How to get list of contents of a particular content type programattically
To create a list of content with filters (e.g. by type) you probably want to use either Views or, if you have a reason to load whole entities by ID rather than individual fields, an EntityFieldQuery.

Since there may be a large number of nodes, this type of use case usually uses an autocomplete field by entity title rather than a dropdown.

To create a dropdown, you'll want to use the core Form API to create a form, and the #options array for the dropdown field would be provided by either the View or EntityFieldQuery you create.