Does doing the "Story" mode in Untold mean I won't be able to choose my own party? And does skipping it mean I won't get any connecting story in the game?
1. Yes, although once they hit level 30 you can Class Change (ala retire) them into classes of your choosing if you want.
2. No. Classic Mode still has the story as told in the original EO1 (which some vastly prefer compared to Untold's), but you won't get all the extended story details (/rewrites in some cases) that Story mode got. The major loss playing Classic is that you can't access Gladsheim, and if you don't play Story first you can't class change into Highlander/Gunner ; but to make up for it you have your own party selection and unlike EO1 Ronin/Hexer are
immediately available as options so go nuts.
Oh, and speaking of things missing from Classic Mode, Famitsu has confirmed that EOU2:
A. has a classic mode
B. that will still contain all the new features being added to Untold 2's Story Mode (the new dungeon, city growth, etc.)
C. will also come with
sixteen portraits per class (the same four designs, but there's variants for each design in different poses, etc.), and
D. will enable you to pick Beast and Princess right off the bat.
In other words EOU2 Classic will be a fully enhanced experience without any catches.