You have a challenging question.
First, integrated amps tend to have terrible headphone jacks. They are afterthought features… often even on very expensive ones.
Sennheiser HD 650 headphones require a lot of power to sound great… so definitely a separate headphone amp. But headphone amps vary wildly in current. To get the current some of my headphones need required me import an amp from Germany a number of years ago.
The Red Dot amps I have seen and heard are very low powered amps and are not good matches for Sennheiser.
Since you like headphones the most, I recommend you concentrate all your effort and funds to creating that system first. If you want the finest sound for the money then it is as much research and effort that a main system will require.
I have owned a dozen headphone amps over the last fifteen years or so. The very best in my opinion is Woo.
Sennheiser, Denon, and many others tend to be hard to drive… but extremely good sounding.
Focal and UltraSonde and some others tend to be very easy to drive.
Hopefully this is helpful. My systems are shown under my user ID.