is this possible to create a vf page which will display a report based on my chosen picklist?

Hi Danna

Yes absolutely it is very much possible . In such tasks which includes custom reporting based on VF page we query all data from the salesforce system and shows complete data on VF page with pagination. Because pagination is needed to display large data sets on  VF page for saving view state size of VF page. Everytime picklist value is being changed then we refresh the data on VF page accordingly.

Hope it helps

Thanks