Air carrier pilot reported lack of lighting and ramp markings made it difficult to taxi and park at the new Terminal A at EWR airport.

Narrative

The new Terminal A (NTA) presents some issues for pilots. First; naming the taxiways with similar sounding call signs as the terminal itself is very confusing. We have Gates Alpha 10; 11; etc.; and taxiway markers Alpha 10; 11; etc. Renaming the taxiways in such a way as to totally eliminate possible confusion would be of great help. Second; taxiway marking visibility. I landed during a rain event yesterday; and the markings were extremely difficult to see; especially considering that the paint is still brand new. We could really use some taxiway lighting on ALL of the ramp in order to minimize safety risks while taxiing. When I made the turn towards the gate; the self-park system was on; but neither my FO (First Officer) nor myself could see the taxi lead-in line for our gate due to the dark and the water on the ramp.It took almost ten minutes to get the Ramp Tower; Operations; and the Ramp Personnel to understand that we were not going to taxi without traditional Marshaller guidance because we couldn't see where to make the turn. This decision was validated by the fact that the self-park doesn't line up with the centerline of the nose of the aircraft. What I thought might be a taxi line was actually something else. Having Marshallers helped; but better lighting or even an in-ground lit marker would go a long way to fixing this potential safety issue. THIS IS ONLY GOING TO GET WORSE DURING SNOW EVENTS!