This is how I'd do it:
Gameplay:
Remains largely unchanged, with minor updates to the materia system and battle system etc.
Leave the basic principles, but add some extra awesomeness. I don't know about random encounters. I'd probably make it so that enemies would be somewhat visible and avoidable to a certain degree.
Transition to battle screen would probably still occur...though if it works without it (as in, normal field environments can be used for battle as well), so be it. Also, battles wouldn't be as static. I imagine something along the lines of FFX-2, where the characters didn't go back to their original positions after making their move but instead the positions of enemies and characters was ever changing.
Limit breaks stay the way they are although increasing the limit gauge by different means (as in FFX) would be a nice idea as well.
I'd handle the summons the same way as they were in the original.
No world map. Yes, you heard me. I'd use the world map for air travel and the submarine only, going by foot would have you wander through large and seamless areas (possibly by clever streaming technology or sth)
Those areas would be highly explorable and filled with monsters, sidequest and n00dz (wait, what?
)
Menus would stay the same including sound effects except they would look a little crisper due to the HD graphics, duh.
Designs would slightly be altered to fit the new compilation designs (like the SOLDIER emblem, Buster Sword etc.)
Music: Rearrangements of all original tracks would be done (possibly by Hamauzu, that'd be awesome) some of them as orchestral arrangements (like the opening, maybe include a couple of exclusive orchestra tracks for certain key cutscenes, new OWA arrangement (because using the old orchestra version like they did in Dissidia would just be lazy)).
Theme song? Don't think so.
Oh yeah, I'd also reduce FMVs to a minimum. We don't need that bullshit anymore, in-game cutscenes are just as pretty on the current console generation (yes, I said current, not next =P) and HD FMVs would use up immense amounts of storage.
Also, Cloud would always be alone on the field, whenever the game switches to a cutscene, the other party members would appear (and they'd ALL be included instead of only the ones you selected for your party)
Minigames! All of them would stay, except more awesome. I'd include extra attacks and other special moves for the motorbike chase especially. =D
A couple of references to other compilation games would also be included.
Uhm, what else...oh yeah, I'd make Vince and Yuffster mandatory characters. I mean, they are canon and I'd say that probably 99,9% of all FFVII fans get them everytime they play the game.
Also, Tifa's boobies would get a realistic bouncing physics engine.
And I support the idea of the characters wearing appropriate clothes for the icy areas in the game.
I'd also include the Modeoheim ruins. Either as an optional area that can be discovered somehow or as a mandatory area that you have to pass through.
The Banora ruins would be included as well (minus the whole final CC area).
