Wow, I am delighted with your diligence and research! Kudos! Yes, the sound of different interfaces in this price range is a subtle and somewhat personal thing. One advantage of the Behringer 204HD is that it has 2 insert channels on the back, not that you would want or need them, but nice to have if you are using outboard compressors or effects.
If possible, please be sure that you have the latest version of Windows because JackTrip is constantly being updated. If you want to use an earlier version of Windows, there are earlier versions of JackTrip that might work but could be a pain to match them up.
How far away is your remote teacher? Under 700 miles would be ideal. Also, a fiber connection is ideal, for both of you, but work with what you have. Any network distributed audio, no matter the distance, have what is called, peering relationships, between different ISPs that can cause noise and latency, and have nothing to do with the JackTrip app.
The internet is a dynamic environment that constantly changes depending on traffic and other conditions. Sometimes we can negotiate JackTrip settings to strike a balance between latency and noise; lower the latency and there could be noise, raise the latency and staying in sync could be challenging. Other times, there is simply nothing to be done. The conditions can change by simply disconnecting waiting a few minutes, even rebooting, and then reconnecting. All slowly and calmly. And with a willingness to address the problem at hand. And to have this attitude each and every time you want to JackTrip.
In any case, we have to give credence to the network and treat it like another member of the group by considering its needs and abilities. You have a ways to go before you will be dealing with optimizing JackTrip and the network settings, but I share this with you now so that you maintain the level of enthusiasm and ready face the potential challenges. Most people want JackTrip to respond instantaneously to any changes or conditions, and while it is pretty good and improving all the time, JackTrip is only as good as the network and the connections to it, including all the audio connections.
Like I mentioned, JackTrip settings and connections need attention to detail every single time BEFORE you even connect. Give yourself 20 minutes BEFORE you connect to check the ethernet connection, audio quality, get logged in, check the lighting, placement of yourself, instruments and equipment, and take a breath, among other preparations. Your teacher will thank you, and you will feel so much calmer. One of my main mentors Pauline Oliveros used to say, “It ain’t like falling off a log!”
I hope that this information is encouraging to you and that you have great success! Please keep us posted on your progress and any questions you might have. You can do it!