I've been to the three starter planets that are given, and by that I mean the moons of them as two are gas giants. I checked the warp lines and there is one branching off of each that goes no where, could someone help me out with this?
You could provide more details on what game/ scenario you are playing. The default survival/ singleplayer has 4 starter planets, and warp is now limited by distance (device/ ship based) and not restricted like with the old pre-galaxy setup.
I'm playing default survival, there are only the three planets and I've further looked into it but they were old posts saying that planets had to be discovered, is this still the case or is what you see what you get?
You need to build a warp capable capital vessel then use the galaxy map to warp to other star systems. All planets in a solar system show up on the solar system map now, so there's no need to discover planets (that's the old way).
To visit moons within your system, a small vessel (SV) with a warp drive is enough; to get out of your system you need a CV like ravien said, this gives you max. 30 light years range for 1 jump. You need to use the galaxy map to set a waypoint by clicking on a sun and 'lock' this destination, you will then see the waypoint appear when you fly, align with it, speed-up to at least 40-50 and hit the warp key.