About the remakes: there are more pertinent differences regarding the game's mechanics and history? How different the game became with the changes to the skill system? Do you recomend to play them instead of the original versions, for a first playthrough?
Yes, the changes to the skill system definitely change the game. For example, in Avernum 1-3, it is actually quite viable to make hybrid characters; for example, characters who can fight well *and* cast spells, or characters who can competently use both types of magic. In Avernum: Escape from the Pit (and I assume the Avernum 2 remake as well), however, you really need to specialize each character in one specific role.
I do not have any recommendation of which version to play, but I personally prefer Avernum 1-3 because they don't force you to overspecialize your characters. With that said, the later remakes do have some quality of life improvements (Avernum 1 didn't even have a quest log, despite having quests given in towns!).
(Also, Avernum: Escape from the Pit is unusual in that money ends up being rather scarce; the Avernum 2 remake apparently fixed that issue.)
In any case, Spiderweb Software is known for providing substantial demos of their games; why not go to avernum.com and try them out before you spend money on them?