The Hall of the House is the subject of Rule IV. It defines the purposes for which the Hall can be used - "only for the legislative business of the House and for caucus and conference meetings of its Members, except when the House agrees to take part in any ceremonies to be observed therein."
In addition the rule lists the people who may be admitted
(1) Members of Congress, Members-elect, and contestants in election cases during the pendency of their cases on the floor.
(2) The Delegates and the Resident Commissioner.
(3) The President and Vice President of the United States and their private secretaries.
(4) Justices of the Supreme Court.
(5) Elected officers and minority employees nominated as elected officers of the House.
(6) The Parliamentarian.
(7) Staff of committees when business from their committee is under consideration, and staff of the respective party leaderships when so assigned with the approval of the Speaker.
(8) Not more than one person from the staff of a Member, Delegate, or Resident Commissioner when that Member, Delegate, or Resident Commissioner has an amendment under consideration (subject to clause 5).
(9) The Architect of the Capitol.
(10) The Librarian of Congress and the assistant in charge of the Law Library.
(11) The Secretary and Sergeant-at-Arms of the Senate.
(12) Heads of departments.
(13) Foreign ministers.
(14) Governors of States.
(15) Former Members, Delegates, and Resident Commissioners; former Parliamentarians of the House; and former elected officers and minority employees nominated as elected officers of the House (subject to clause 4).
(16) One attorney to accompany a Member, Delegate, or Resident Commissioner who is the respondent in an investigation undertaken by the Committee on Standards of Official Conduct when a recommendation of that committee is under consideration in the House.
(17) Such persons as have, by name, received the thanks of Congress.
All other persons are to be excluded from the Hall and its Cloakrooms. There are limitations on the rights of former members when they are lobbyists.
The Gallery has special areas set aside for certain people (Rule IV 6)
An express provisiom forbids the knowing distribution of political campaign contributions within the Hall or the rooms leading to it.
There is a short article about the Hall here.