@Darkandstormynite
We are in such uncharted (and unimaginable to our Founding Fathers) territory that concrete answers to many questions can't really be given.
All we know is that the only Constitutional requirements for POTUS are to be 35 years of age, be a 'natural born' US Citizen, and having been a US resident for 14 years. I think the FF simply couldn't imagine that a convicted criminal would ever stand for POTUS.
A conviction AND removal from office by the Senate after impeachment in the House 'bars' a return to the presidency and is the only 'sure fire' bar as it is not appealable. Any other 'bars' to holding office are in other parts of the Constitution (specifically Article 14), don't specify the Presidency, and have never been tested in a court of law. Removal/bar based on the 14th are appealable (as we are currently seeing).
FWIW here's the basis of all the 'wrangling'. Article 14, Section 3.
No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any state, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof But Congress may by a vote of two-thirds of each House, remove such disability."