Ask me if you'll have some difficulties in game, and I'll add more advices on that matter here.

Staying alive

There are lots of ways to avoid being killed in Void.

Be fast. Use fast ship (i.e. light and with powerful engines), and invest in Navigation skill. You got 5 free levelsin it from the beginning for a reason.

If your ship is fast, it will be easy to you to pursue, and more importantly run away when needed. And you will need to run away a lot. 

Learn to use stations. If you see a dangerous ship attacking you, fly to nearest station. There you can wait for any nasties to fly away. Or at least replenish your hp. 

Avoid being shot. Guided missiles can be shot down with your own weapons, non-guided weapons can be dodged. It's easier to do it when you are far from enemy, so try not to get too near when his/her energy is high.

Stay in part of sector where enemy is not too strong for you. There are generally more technically advanced stations in lower right corner of sector, and less advanced in top left. Enemy ships from advanced stations use better equipment, and therefore are more dangerous. So, if you feel enemies are too hard for you, move to top left corner, and vice versa.

Ealy game

Your ship and skills are not that great at the beginning, so there are some ways to get money and exp early on.

Hunt small and weak ships. It's possible even with your starting ship, and will give some exp/money.

Do delivery contracts. Take several delivery quests at once, if you have enough cargo space.

Browse every station and buy better equipment if you can find it. Especially - better engines.

Do escort contracts. If they are between nearby stations, there are chances that no one will attack ship you are escorting.

Stay in top left corner of the map. There aremuch less powerful enemies there.

Contracts

Delivery contracts. They are probably esiest of all. You can start doing them from he first minutes in game. Not much to say here, except that don't hesitate to take several delivery contracts at once. You will need some free space on your ship,though, as some parcels are rather big.

Collect. Similar to delivery, and also can be done yearly. But require a bit more flying around and you'll certainly need a big cargo ship for them.

Eliminate. Note tech level and hull type of the target. Small ships will be usually easy to hit.

Escort. Probably most interest/annoying mission. Take them if you are strong enough to kill anyone that would attack escorted ship OR if escorted ship is fast or strong enough to survive attacks OR destination is not far away. Note, that if you dock to a station, escorted ship will to. That is the way to hide before heat will fall.

Elite rating

As you kill ships (preferrably strong ones), your rating raises. Bad news is that other ships skills will raise too, making life hard. So keep your skills on par with your rating.

Also, each to levels of rating, tech level of all stations will rise by two. That will improve stock available and other ships equipment.

One last thing that will raise is contracts rewards and kill rewards (both exp and money).

If you feel that enemies are becaming too strong  for you after level raise, move in NW direction and do some missions (and abstain from killing) to compensate equipment/skill difference between you and enemies. And if you feel that enemies are too weak, move to SE corner, and kill some people.