What other things do you want the power for?
If it's not that important, unless you've got an annoying one like my large Dell, you should be able to use a universal car adaptor.
This will save you getting an inverter and have less losses - probably less losses than your 240v charger too, as it's just DC to DV with a fairly similar voltage (however, probably will depend the technique used.)
DC is also fine for running lights and various other things, but less flexible than an inverter.
How often do you expect to be driving? If you're driving every day and charge the laptop up while driving, you should be fine with just one extra small battery, if that - I've done similar with a motorbike and with riding every day have had enough charge to use a netbook in the evenings, worst case running the bike for a bit - for the cost of a solar panel and controller, you can run the engine for a good long time!
A solar panel of course can't be relied upon to give decent power all the time.
Your laptop is quite low powered 45w or so - unfortunately mine is over 3 times that.
One thing you could consider is just getting a few spare laptop batteries and charging these from your van battery with the engine running - maybe with a hobby charger to give a decent charge while doing them all at once.
If this all you need, saves money for fuel for the mx bike (nice choice on fun things over living accommodation by the way - a fair bit of the last ten years have been like that for me too
).
Back to having a working 240v solar powered system, which is what I've currently got.
The best value panel I've seen is a 290w from bimble solar for £166 + £30 delivery (but you save on deliverly if you get multiple - when I have some cash to splash I hope to get 4 thanks to a large roof).
You will need a mppt controller to go with that.
If you get a 12v panel you can get away with a pwm controller, but if you use it with a 24v on a 12v system you'll lose a lot of power.
For the leisure battery, bigger is always better.
Ideally go for a true deep cycle one - most marketed as 'leisure batteries' are just car starter batteries with a different sticker.
Flooded lead acid (not sealed) is the best value.
6x 2v single cells can be got fairly cheaply and will give you loads of power that will last you a long time in bad weather with no solar. But will weigh about 200kg - when you get the rest of a conversion done, that might not leave you with much weight left.
Trojan 6v batteries have a good reputation too; go for the 're' versions if you can as they work better to low discharge.
My current favourite choice for "when I have money" is Elcosol 270ah batteries, but they have a mixed reputation.
For the inverter; go for a pure sine wave if you can.
If you don't need a big one, don't get one; a small one won't use as much and will be more efficient for a lower power output.
Modified sine wave my make your power supply buzz a bit - but are cheaper.
The cheap Chinese ones are just that - my 1000w cheap chinese one is under half the size and weight of my 800w one from Maplins - the latter is 24v, but that actually means it should be smaller as there's less of a difference in voltage I believe!
However, the cheap one does power a laptop ok - but the fan is always on, while the Maplins one only has it come on when hot.
I just tethered internet through my mobile and been fairly happy with that so far - £1 a day extra to tether through Orange outside my first 1.75gb. Costs me about the same as if I had phone+broadband at home. I used something like 36gb last month. (Panther plan on orange - other plans you'll end up paying £2 per day.)
I have been looking at long range wifi aerials recently - there are ones that claim better than 12dbi for less money on ebay. I'm presuming you realise that you don't need a wifi aerial if you're doing it through a dongle or your phone?
