ADS1115 ADC input filter - active or passive?
Summary:

A band pass of 300Hz to 1MHz won't do you any good - the ADS1115 can only sample at maximum 860 samples per second.
You cannot capture a signal above 400 Hz with the ADS1115.
TI recommends a simple RC low pass filter to reduce aliasing.
An RC low pass is adequate because the ADS1115 samples at a much higher rate and decimates and filters down to the set output sampling rate.


Details:
As always, start with the datasheet
The ADS1115 will be of no use for a signal between 300 Hz and 1MHz.  It has a maximum data rate of 860 samples per second - that's just about adequate for signals up to between 300 and 400 Hz.  Above that you will get aliasing and a much reduced signal level.  In other words, you can sample signals up to about 400Hz with the ADS1115.
All you need is a low pass.
On page 33, you will find this recommendation:

A first-order resistor-capacitor (RC) filter is (in most cases) sufficient to either totally eliminate aliasing, or to reduce the effect of aliasing to a level within the noise floor of the sensor. Ideally,any signal beyond fMOD/ 2 is attenuated to a level below the noise floor of the ADC.  The digital filter of the ADS111x attenuate signals to a certain degree,as shown in Figure21. In addition,noise components are usually smaller in magnitude than the actual sensor signal. Therefore, use a first-order RC filter with a cutoff frequency set at the output data rate or 10x higher as a generally good starting point for a system design.

fMod is the modulation frequency of the delta-sigma converter in the chip.  It is the effective sampling rate that the signal &quot;sees.&quot;  In the ADS1115, fMod is 250kHz.  To avoid aliasing, you need to reduce signal content above 125kHz.
The ADS1115 has digital filtering to remove stuff between the final (output) sampling rate and fMod/2.
An effective filter starts at your selected sampling rate.  If you are sampling at 860 samples per second, the you need an RC low pass with a cut off of 860 Hz.  For example, 1.6k and 100nF provides a cutoff of 884Hz and an attenuation of about 45dB at 125kHz.