Open Files in selected application

Most apps will allow the transfer of files to the iPad via iTunes. Click The apps tab on iTunes with the iPad connected and at the bottom, you'll see a place to select your app and then attach files for transfer.

Tell us what file types and we can give you more specific help..

But ad a rule on iOS you dont have a finder or access to a file system

Is there a way to transfer files to the iPad and them open them with the application of my choice?

If you email the item, open it in Mail on the app then select the attachment and tap and hold the attachemtn then select Open, you should get a list of apps that can open that document.

Would a cloud storage app, like SropBox or SugarSync, work? they would allow you to sync folders and their Docs to the iPad, and you can view them in a finder-like format. Not all apps can open from these apps, and some let you open but not save into the folder structure, but they might fit your needs.

It is just that I would like to have a system like "Finder" available so I could see all my various documents in one list.

This is not possible.
Because apps are sandboxed, which prevents data or files from being accessed by other apps. Helps to prevent data corruption and malware.
From the iOS Application Programming Guide
Security
An important job of iOS is to ensure the security of the user’s device and the applications running on it. To this end, iOS implements several features to protect the integrity of the user’s data and to ensure that applications do not interfere with one another or the system.

*The Application Sandbox*For security reasons, iOS restricts each application (including its preferences and data) to a unique location in the file system. This restriction is part of the security feature known as the application’s sandbox. The sandbox is a set of fine-grained controls limiting an application’s access to files, preferences, network resources, hardware, and so on. Each application has access to the contents of its own sandbox but cannot access other applications’ sandboxes."