Do you think that the compromise creating a two-house chamber to balance the needs of smaller and larger states was the best solution? explain.

It was a brilliant solution. It was a combination of a democracy (The House) which addressed the concerns of the people and an oligarchy (The Senate) which addressed the concerns of the States. 
... and was totally undermined by the adoption of the 17th Amendment. 

The House, with representation by population favored the large States; while the Senate, with each State having two representatives, favored the smaller States.