My requirement is to create testcases where i have to validate the data on the screen ( web app) and the modified data in the desktop app, based on actions performed in the web app. In some cases, i have to match the data in the web app with that of the desktop app.
Which project should i choose for my requirement and can my requirement be solved without involving any scripting.
I'm not sure what you mean by which project to choose? If you're refering to what to select in wizard, it doesn't really matter. As long as you have the required modules installed, all aspects of Test Complete will be availble regardless of what you select in the wizard, it just sets up some defaults for the type you select.
As far as your requirement being solved without any scripting, I am not sure at all as I don't know what your requirements are. Likely it's possible to do what you need to without any scripting, but it might get really messy.
Especially when dealing with a lot of data, writing helper scripts to call in your keyword tests is almost always the best approach.
The wizard for creating a project does not lock you down into only being able to test a certain type of application. It simply generates the "Default" project items for that type of application. You can test any and all application types within the same project so long as you have the license to do so.