I've searched a lot in the forum finding several answers to part of my problem. In brief I need to make some computation keeping in account the distance from every point along different angles until a distance of 25 km. The resolution of raster from which I'll extract data change as step function of distance from the point analyzed. It goes from 1m in a narrow zone (1 km) to around 90m (until 25 km). The zone is Europe. This give an indication on the accuracy I need. Initially I've been starting using UTM implementing in the code the simple capability to select the correct UTM zone. To minimize distortion when I get closer to the UTM zone limit (or higher lat) I'd like to change approach implementing a TM projection in Elliptical form centered in the area I'm analyzing that should means define as central meridian of grid origin the mean values of LON of the area considered (solution partially suggested by this answer of @whuber in Measuring distance in spherical Mercator vs zoned UTM).
How can I build the projection string in a parametric way?
My main problems, cause my limited knowledge in this topic, is about some parameters as +k +x_0 +y_0 (Scale factor at natural origin, False easting and False northing). The CRS string should appear in this way if I'm not wrong:
"+proj=tmerc +datum=WGS84 +lat_0=0 +lon_0=b +k=? +x_0=? +y_0=? +units=m
+no_defs +ellps=WGS84 +towgs84=0,0,0"
with b the mean lon of the area analyzed. For my knowledge false easting and northing should only affect the sign of coordinates but +k? Can I set +k as 1?
Is the approach correct? It is better to choice a different map projection in my case?