What each option changes

SettingEffect
NormalThe less demanding battle difficulty.
HardThe more demanding battle difficulty.
CasualDefeated allies return after a battle.
ClassicDefeated allies are lost permanently.

Can you change it later?

The Obelisk Chamber allows Hard to be lowered to Normal during a path. Raising that path back to Hard requires replaying its prologue. Pick the higher battle setting only if you want to keep that challenge; make the Casual/Classic choice with the same care at the start.

A first-play choice

Normal with Casual gives room to learn Free Time and recruitment. Hard and Classic can be combined for a stricter run. The two choices are independent; harder maps do not require permanent losses.