So, we know from the backstory that the various Legacies each have all the powers of their father plus one more, so I thought it would be fun to try and figure out the different historical versions and what they could do. Here's a list containing what we absolutely know:
Joseph Parsons (b. 1759): Danger sense.
Paul Parsons (b. 17??): Danger sense, enhanced speed and sight
Paul Parsons Jr. (b. 18??): Danger sense, enhanced speed and sight, maximum human strength
Paul Parsons III (b. 18??): Danger sense, enhanced speed and sight, maximum human strength, ?
Paul Parsons IV (b. 18??): Danger sense, enhanced speed and sight, maximum human strength, ?, ?
Paul Parsons V (b. 190?): Danger sense, enhanced speed and sight, maximum human strength, ?, ?, flight
Paul Parsons VI (b. 193?): Danger sense, enhanced speed and sight, maximum human strength, ?, ?, flight, ?
Paul Parsons VII (b. 19??): Danger sense, enhanced speed and sight, maximum human strength, ?, ?, flight, ?, ?
Paul Parsons IV (b. 1973): Danger sense, enhanced speed and sight, maximum human strength, ?, ?, flight, ?, ?, Impenetrable Skin
Paulina Parsons (b. 1993): Danger sense, enhanced speed and sight, maximum human strength, ?, ?, flight, ?, ?, Impenetrable Skin, Atomic Glare
(I'm assuming that the 1900s-era first Legacy was Paulina's great-great-grandfather, though it might only have been her great-grandfather, America's Greatest Legacy, if he had waited much longer to have a kid than America's Finest Legacy did, with Great's son and Finest's father having done likewise, and was about Finest's current age when he fought in WW2. It depends on how old the latest two Legacies were when they reproduced; 30 years apiece seems like a decent eyeball, with Newest born in 1993, Finest in 1973, some unidentified intermediate in about 1950, Greatest in 1930 or earlier (in order to have been of legal age in WW2), and the first flying legacy in the first decade of the 20th century. It seems that the entire 19th century contained only four Parsonses, including the very first Paul, who must have been born in about 1890, very late in Joseph's life, and likewise waited a long time to have Paul Jr. who in turn waited a long time to have Paul the 3rd…Paulina's father must have been unique in breeding at the age of 20, since if they'd all done that, he would have been about Paul the 11th instead.)
So we're left with four "blanks", two before and two after the first appearance of flight. One of these must be filled with "super-human strength"; Paul the 2nd was supposed to have strength "equal to all but the stoutest of men", which is obviously not the same as AFL's ability to catch plummeting monorails. I would theorize that another of these "slots" could be filled with "remarkable charisma", as that seems to be an ability consistent with the superho archetype these guys are playing into, though it could be argued whether it actually counts as a superpower. That leaves a couple of powers unaccounted for, so I thought it would be fun to speculate about what these abilities might be, and which member of the lineage they first manifested in; they need to be consistent with the observed powers of "our" Legacy (for instance there's no evidence that he has X-ray vision). I'm going to toss out two theoretical choices, which you guys can freely shoot down: superhuman speed (again, a low-grade version of this seems to have been present in Paul the 1st, but by the time it gets up to what we see on Take Down, it's clearly been improved), and in one of the versions that didn't yet have super-strength or impenetrable skin, perhaps a form of "inertia immunity", thus that he couldn't bounce bullets off his skin, but would at least not be knocked down by the force of them. This might also substitute for his super-strength; perhaps he can't actually LIFT a train, but just can STOP one from falling. Another interesting possibility is that in one generation, he might have first gained super-strength, but applied it in a realistic manner (ie if he picks up a train car, all the force necessary to lift the train's weight is being applied to one hand-sized spot in the middle, so the train either cracks in half or gets a human-sized hole punched through the middle)…so that the next generation's power would be something akin to what the 1990s version of Superboy referred to as "tactile telekinesis", the ability to move an entire object by touching just a part of it, essentially creating an energy field around it which holds it together.