How to convert proprietary ESRI geodatabase to open standards and consume data in a web service?

I have a ESRI file in geodatabase format (v9.3). I intend to use this in a non-commercial application. I think I will have to convert it into a open standard since I am confused if ArcGIS online would need a paid subscription even for a non-commercial 'production' application. (Please let me know if i am wrong about their developer license)

So I am here basically looking for a solution to convert the gdb file/directory to another open format and do below operation: I need to use the gdb data (available data is polygon map overlays) to derive connecting lines from mid point of one polygon to the other polygon. (there would be a huge number of sets of two polygons like this). The end dataset would be a single table having below columns

set_id, line_start_point_lat, line_start_point_lon, line_end_point_lat, line_end_point_lon

and I plan to use this data further in any open standard (google maps/ d3.js - still need to figure out); to use in my website to draw lines as map overlays connecting these points.

Could anyone tell me what open source technologies I should be looking at to convert and do above operations?