If we were to enter into a new star system, what are the important properties which you would want to determine in the system?

Define your "new star system" vis-a-vis any star system. I am a dull head that don't understand what your learned self says.

The type of each planet in the system; rocky, gas giant, hot jupiter, hot neptune, etc.

For each rocky type planet (if any), the surface temperature range, components of the atmosphere, existence of liquid or frozen water, signs of life (if any).

The star's age, type, absolute brightness, variability, mass, harmful radiation spectrum.

Stellar mass, age since formation, spectral type, stability of any planetary system present.

Then how do we leave and reach the next system, or return home.

Cheers!