US Congress has two houses, Senate (called Upper house), House of Representatives ( Lower). When a bill is introduced, which house is it supposed to be first or can it be introduced in either? Are there bills that only a single house need to approve?
Bills may be introduced in either house of Congress. On the website of Congress you can search for recently introduced bills. You can see that some of them start with "H.R." and some with "S." depending on where they originate. There is only one exception in article 1 section 7 of the US Constitution:
All Bills for raising Revenue shall originate in the House of Representatives; but the Senate may propose or concur with amendments as on other Bills.
There are some powers that the Senate has that the House doesn't, particularly those in article 2 section 2:
He [the President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
On those matters it does not matter at all what the House of Representatives says.