For all the major brands of laptops you can get a dual voltage power supply. These take either 110v AC or 12v DC as their input and convert it to the required voltage for the laptop.
This is what we provide all our uses with their Dell computers. It does 110 - 240 v AC, 12v DC and also has the special adapter for the power found at the seats in some airplanes.
http://accessories.us.dell.com/sna/prod ... u=310-8814

You can find similar products from all major laptop producers.
There are also many of these 3rd party products on the market
http://www.laptop-battery.org/Adapter/index.htm
All of these allow you to skip the AC inverter and it's losses and just make a simple DC to DC conversion.
The inverter will also work just fine.
In general most laptops run on 16v to 19 v power. You can easily tell by looking at your current power supply. It will be clearly marked with both input and output voltage. For instance, the laptop I am typing this on right now has an input rating of 110-240v at 1.2 amps and an output rating of 19v at 2.1 amps.
Voltage times amps equals watts, so if I were to plug this into an 110v inverter the maximum wattage it would draw is 110v x 1.2a = 132 watts. In reality it draws far less as it is only asked to produce 19v x 2.1a = 39 watts. There is loss in the conversion, but as you can see the load is still small. I have run every laptop I've owned (many different brands) without any issues on my 110v 150 watt inverter.
You should have no problem at all with a 300 watt inverter.
For the laptop I'm using I would expect it to draw around 60 watts with the conversion losses. From a 12v battery, 60 watts is 5 amps per hour of use.
You should work up a electrical budget in amp hours that accounts for all your electrical use in a day. It would look something like this
Edgestar Fridge, 4.0 amps at a 50% duty cycle = 24 hours x 4.0 amps x .50 = 48 amp hours
Lights, 1.0 amps x 5 hours = 5 amp hours
Stereo, 3.0 amps x 2 hours = 6 amp hours
Laptop, 5.0 amps x 2 hours = 10 amp hours
Pumps, 7 amps x 1/2 hour = 3.5 amp hours
For things not used every day come up with a daily average
Add them up, in this example, 72.5 amp hours x 12v = 870 watts a day.
You can expect a 120w solar panel to reasonably produce an average of 60 watts of 12v power for about 15 hours a day. This is 900 watts of power on average. In this example your budget is balanced. Now go plug in your own numbers and see what you get.
When calculating what your batteries can supply, take their amp hour rating, say 100 amp hours for a Group 27 battery, giving you 200 amp hours with the 2 batteries. You should never discharge a battery below 50% of it's capacity so that means you have a 100 amp hour supply in your batteries to supplement your solar production.
On batteries alone you have just over a 1 day supply of power, 72.5 amp hours needed and 100 amp hours available. Going two days on batteries alone would discharge the batteries too far and doing this often will damage them.
If when you do your budget you come up 10 - 20 amp hours short of your solar production you could reasonable expect to be able to supplement this from the batteries for 5 to 10 days before you need to charge from some source.
If you run your engine daily traveling take about 50% of it's rated alternator output in amps times the number of hours under way and add that into the equation.
You also want to be sure you have a proper sized charger on board. If you are going to pull into a dock in the afternoon, say 4 pm, and are 100 amps down in your battery bank, with a 5 amp charger you would need 20 hours plugged in to fill the bank. You better plan on staying at the dock two days. With a 12 amp charger (what we have on board) you could bring the batteries back to full in just over 8 hours. In reality it takes longer to refill than the simple math shows, but you get the idea. A small 5 amp charger means you are tethered to the dock for 2 days at a stop while a medium sized one lets you leave the next morning. If you add more batteries creating a bigger bank and a larger deficit when you arrive at the dock, you need a bigger charger to get things full again in a reasonable amount of time.