I do not know whether i can help or not but i can tell a thing or two about this. Perhaps, that would help you to decide to some extent.
Both Ramayan and Mahbharat are neither philosophy nor religious books. They tell the life stories of two Avatars of Lord Vishnu, who is one of the Hindu Trinity. The other two are lord Brahma and lord Shiva.
Ramayan is all about ideals. It tells how to behave ideally in the society. It defines all relations. A father, A son, a mother, a daughter, A brother, A friend, A husband, A wife, a king, a Guru etc. This is to say that it does not spare any relation of the society.
Mahabharat is quite similar, more or less. But, it does not live in the completely idealistic world. It has more grey area than Ramayan and more closer to reality. Its main character, Lord Krishna, does not hesitate to use slight unjustified means to achieve the just goals, which is complete no-no in Ramayan.
Secondly, its canavas id very large, far more than Ramayan. It is said that here cannot be any such incident in the world ever, that is not already described in the Mahabharat.
Thindy, as you know, Gita is a small part of Mahabarta and its crux too. It is pure gold, if one can grasp it.
To be frank, Hinduism has no particular religious book like Bible or Quran.
I thinkthat it would be useless to real Vedas. You will not get anything from those.
If you want to read some philosophy, then you should go for Upnishads, which are commentories on Vedas. Contrary to the general perception, Upnistads are pure philosophy, not some religious texts.
If you want to read it, my suggestion would be to go for Mandukaya Upnishad to start with. It is the shortest one yet quite enough. You should find its english tranlation by Swami Nikhilananda, which is available on the net.
At last, i think that you should read in this order- Ramayan- Mahabharat- Gita- Mundukaya Upnishad.
Good luck.
with love,
sanjay