Some great advice above. Key points for PvE healers,
1. Start with recruit (it's free!)
2. Aim for the 2 piece set bonuses from both the PvP and PvE field medic sets.
3. Run dailies for earpieces and implants (and cash, and BH comms).
4. Don't kill yourself grinding the War Hero relics, the Champion ones are pretty good and only 11,300 credits.
5. Plug holes with Black Hole items.
That should get you started, and shouldn't take too long to acquire. Once you have that, you should have a really good idea what you want / need. Then you can start augmenting, improving, min/maxing, dropping the expertise, mod swapping, etc.
And refer to Dulfy's excellent guide here
and play around at Mr. Robot
's character builder.