Ohms Law can be used to roughly calculate your needs.

300 Watts at 14.4V (The most that will be coming out of your lighter socket when your car is running) constitutes 21 Amps...could be more or less depending on how your inverter is rated as there are losses internal to the inverter circuitry. If it's rated at 12V, then it's going to need 25 Amps! Your manual or the label on the box may even tell you what it's maximum current draw is at peak. One other thing to consider is that if the inverter puts out that 300W steady or peak. If it will handle 400W peak and you ask it to deliver that much, then you're taxing your vehicles circuitry even more for a brief time.

21A+ is more than any lighter socket I'm aware of. The one in my Jeep is rated for 20 but I wouldn't dare put that much through it. Even running much less powerful devices through it, the socket and the wire get plenty warm.

This is why most inverters that size and larger include wires to either connect it permanently to the car direct to the battery wiring or with alligator clamps to connect directly to battery terminals.

NOW. That being said, your notebook likely doesn't draw more than 100W which means you should be fine on your lighter socket for what you need. I run my 400W one off of low power circuits (fused for 10A) all the time.

The 75 Watt one would run in any lighter socket perfectly fine but might not be enough to run your notebook power supply. Check what it's rated for (it will be printed on the brick) before you use it.