Concept:
The reaction is a nucleophilic substitution on Methyl Bromide. The solvent CH$_3$OH is polar protic. In polar protic solvents, nucleophilicity increases down the group (larger size, less solvation) and decreases with electronegativity/stability.
Step 1: Analyze Halides.
In methanol (protic), larger ions are less solvated and thus better nucleophiles.
Order: I$^-$>F$^-$.
Step 2: Analyze Oxygen Nucleophiles.
Ethoxide (C$_2$H$_5$O$^-$) vs Phenoxide (PhO$^-$).
Ethoxide has a localized negative charge, making it a stronger base and stronger nucleophile than Phenoxide, where the charge is delocalized via resonance.
However, I$^-$ is generally a better nucleophile than alkoxides in substitution reactions due to high polarizability.
Step 3: Combine Order.
I$^-$ (Highest polarizability)>C$_2$H$_5$O$^-$ (Strong base)>PhO$^-$ (Resonance stabilized)>F$^-$ (Highly solvated/High electronegativity).
Conclusion: Option (3).