The more intense peak allows you to lower the signal-to-noise ratio, hence your detection limit. Anyway, you should always keep in mind that other substances spectroscopically may interfere with your analyte, because these wavelengths are not specific for acetylsalicylic acid.
So there is no general answer to your question, the correct answer depends on your concentration range and your analytical matrix. The highest peak may be not the best.
If you are planning HPLC, you should remember that solvents or buffers may be UV active at your given wavelength and that you may have high background absorption. So I recommend to buy HPLC grade solvents with UV spectra in their certificate.
From experience, I would choose 225 nm unless there is a good reason not to take it.
The best wavelength to use would entirely depend on the technique you plan to use and the amount and number of other compounds which may be present in the sample. The preferred detection wavelength(s) may vary.
Example: For UV/VIS work, such as liquid chromatography, we use the lambda max for Acetyl salicylic acid which is about 265 nm. *You can also monitor ~205 nm at the same time for the presence of decomposition products too.
In case you have more than one peak, you should choose the one to use depending on its intensity, and sensitivity towards concentration changes - i.e. more pronounced response to concentration. At any rate, you should try it in the same conditions that you plan to carry out the analyses. From your peak choice, 225 nm would be a better option, as 190 nm is "on the border" of UV.