Instead of providing for a two-term limit, the 22nd Amendment, ratified in 1951, adopts the Mexican model, known as the
Sexenio, under which the President is limited to a single six year term, with no possibility of reelection, either consecutively or not. Also, no person who held the office even on a caretaker basis is permitted to run for or hold the office again. Furthermore the amendment abolished the office of Vice President. President Truman was exempt from term limit under grandfather's clause.
Rules of presidential succession:
* Until Congress names a new President, the Secretary of State (or the next person in the line of succession if the former is not eligible) becomes the Provisional President of the United States, enjoying all the powers of the office. The Congress has to elect his permanent replacement within 60 days.
* If the vacancy occurs in the first two years of the term, Congress elects the Interim President of the United States. The election elections must take place in no less than 14 months and no more than 18 months after the vacancy occurs, with the winner completing the original term.
* If the vacancy occurs in the last four years of the term, Congress elects the Substitute President of the United States to complete the term, after which the regular election is held.
The rest is, of course, up to you. Make your lists