Great advice here about accepting missions, exploring, etc. PvP is mighty aspirational to mention at this sate, imo. You'll certainly get there if that's what you're after, but in the meantime:
take your time,
learn how the game works, how things happen, how potential foes (NPCs, security forces, etc.) behave, how to earn credits, how existence goes,
pick up all those goodies you'll find at USSs along your travels in the Bubble,
get to know how ships maneuver, react, etc (this is immensely useful),
learn how to dock reasonably reliably,
join a group if you'd like some company while learning,
try LOTS of things,
evade an interdiction attempt against you (great accomplishment),
don't fly without rebuy!
have fun!
ask questions here (as already suggested).
I can only attempt to answer your question about where to go next. This is a 3D galaxy, so the answer to this question - in part- depends on where you exited the starter zone. It depends upon range of your ship and your confidence in the Gal Map - whether you're reading it well enough to feel comfortable that it is telling you that you'll make it, among a couple of other details. Be conservative for a bit. When I was new, I accidentally lost access to the starter zone too because I was confused by symbols that didn't clearly (to me) show systems therein, exiting from the
Sharur System and landing at a station in the
Ambibates System.*
From there, my notes show that I traveled to the
Ehecatl, HR 8061,
Ay Indi, and
Veroandi systems. In particular I made a note that says the trip from
Veroandi to
Ay Indi pushed my range limit. I would grab a unit or two of tea, perhaps biowaste, a courier mission here and there. This earned me some credits and the chance to travel and visit 'things' I encountered, learn my cockpit and ship's controls, and on, and on.
If you really want to taste combat with your currently woefully unprepared ship, you can go to a Low RES**
with an empty cargo hold and try just to stay on the tails of other ships to learn maneuvers and flying. You can observe the activities there safely. Combat is a big topic so be very careful at this stage. You won't get attacked if you do only what I suggest in these three sentences. If you can resist the temptation to engage, you'll be safe against the NPCs*** there.
For now you should be able to choose the closest populated system and check out the station(s) there, see what is offered, and decide what to do in terms of missions, trading opportunities, or simply grabbing some repairs/fuel and moving on. You can simply go back and forth between two or three systems/stations for a little bit just to fly, pilot, succeed for a bit.
If you'd like more specific advice or a companion, ask here, look up a group for help, even ask for a sit-in on someone's ship to watch them for a touch. You'll get it in this game. It's pretty darn cool that way.
Happy travels!
* This is accurate or pretty close, as long as memory and notes serve me properly. EDIT: I peeked at the galaxy map and this appears to be accurate.
** A
RES is a Resource Extraction Site. It's a region in a planet's rings where mining activities and piracy are common. These are rated in 4 levels of intensity/danger from Low to High and Hazardous. The designations are: Low RES, RES, High RES, and Haz RES.
*** NPC = non-playing character. These are the game-generated population of pilots & ships NOT REAL CMDRs! (an essential distinction, to put it mildly)
.