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It is a good idea to start with a With, which does not permit the renaming of initial local variables, then Migrate to a Module as needed. It's not just that With uses slightly less overhead (mostly, depends on the Expressions used), it promotes a slightly different workflow, by making it exactly clear what is an "input" (other than the function args) and what depends on those local variables.
f[y_] := With[
{ x = 1.234567 },
x y
];
If you need to upgrade to Module because you've changed a local variable within the scope of a With, it will warn you:
f[y_] := With[
{ x },
x = 1.234567^y; (* ERROR: Attempt to set local With variable *)
x + x^2 + x3
];
With::lvws: Variable x in local variable specification ...
f[y_] := Module[
{ x },
x = 1.234567^y; (* OK: inside a Module *)
x + x^2 + x^3
];