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It is possible to use any ship to fly in null-sec and type of ships can be bought there. It is better to ask some other player you know or a co-Ally to ascort you there. The ship shold be equipped with MicroWarpDrive (MWD), warp stabilizer,  inertia stabilizer (in low slots). To have a  cloaking device would be good, too. It is better to drag the Local channel into a separate windows - this will be very helptul.
As you reach null-sec zones, you should first look at Overvew or simply look around to see what the situation is. If all is clear - jump to the next gate.
Do not attack anyone during flight, do not use smart-bombes, drones and ecm burst either, otherwise you risk to be seriously punished.
If you can see unfriendly ships after the jump, you should zoom out quickly and look for a large glowing sphere (tube) around. If there is no such tube, it is better for you — your ship can be only cought by other ships. Since you have inertstabs, your ship will turn for a jump very quickly. If you have warpstabs, you can also neutralize some enemies hunting you.
Then you should select the closest celestial body to the ship (better in the direction of movement in order to reduce the turn) and jump away 50-70 km. If there is a tube at the gates, you should wait until there will be noone at the range of 10 km. and turn on MWD. Due to the inertstabs, the ship should speed up quickly and the probability of jumping will be fairly high.
If there are enemies at the gate, you should better retreat and scan the gate without applying overview settings. If scanning shows that there is no Mobile Warp Disruptor or Warp Probe, you can safely jump into the gate.
It is even better to do so - double click in the selected direction and activate mwd and cloak. This will result in the following - your ships will appear, speed up and instantantly disappear. When you are out of any risk, you can safely fly far away, remove the invisibility and jump.