What are the formal qualifications for someone who wishes to serve in the house of representatives? how do those compare with the qualifications for serving in the senate?

Both have to be US citizens. For house of rep. Must be at least 25 years old, have to be a U.S citizen for the past seven years, and be at the time of the election an inhabitant of the state they represent. Senate you have to be at least 30 years old, U.S citizenship for at least 9 years and residency in the state a senator represents at time of election