Reverse phase is the standard in HPLC so, if you can use reverse phase do not complicate matters.
Normal phase usually gives more problems than reverse phase and the stationary phases degrade faster.
Reverse phase works fine and in this case you would typically use a C18 column and water and acetonitrile.
In the case of salicylic acid and, in general, all the acids and phenols, the peaks in reverse phase are normally broad and the retention times vary.
That is because there is an equilibrium between the acid and the ionized form, the carboxylate (or phenolate).
To avoid that, you have to force the equilibrium to the acid form, which is also more apolar, so the reverse phase makes even more sense.
For this, it is sufficient to add a small amount of acid to the water used in the mobile phase.
Very often, 0.1% formic acid is enough.
Sometimes it is required to use higher concentrations up to 1%.
If you need a higher $\mathrm pK_\mathrm a$, you can use trifluoroacetic acid instead.