Best way to connect coax along a microstrip
What is the best (=best coupling to the circuit) way I can make the connection in this situation?

The best = 'lowest loss coupling' you can make to the microstrip is to cut a small section out of the microstrip track with a scalpel. Then connect the end of your coax to the half of the strip that you want to inject the signal into. Connect the ground of the coax to the local ground of the microstrip (sometimes easier said than done, but just as, if not more, important than connecting the signal). When you're done with your signal injection experiment, remove the coax, and bridge the gap with a capacitor of few pFs or a piece of foil.
The best = 'most predictable coupling without cutting the microstrip' is to connect a 500 Ω resistor between the midpoint of the line and the end of your injection coax. Terminate the end of the coax with 50 Ω to ground, and connect the coax ground to the local microstrip ground. This will give you a significant signal attenuation, but it will be flat with frequency, and will disturb the microstrip only minimally. Used the other way round, this is an excellent way to monitor signals on a microstrip without disturbing the conditions there too much.
Just soldering the coax onto the microstrip will get your signal on there. However the mismatch will mean that the loss could vary from nothing to lots as the frequency changes. Anything feeding or driven from the microstrip line may be upset by the mismatch.