Yep, good point - and quite likely if your website is on it's own (non-shared) IP address. One way to work around this would be to create a .htaccess file to redirect any requests not matching your domain name to your own :)
I have a couple of laptops with I use heavily for dev work. Dell and Acer, and both have really impressed me.
The dell also has a docking station which connects 2x widescreen monitors on my desk, which i find highly useful as trying to code on 1x small laptop screen can be restrictive at times.
i'm no accountant but i'm pretty sure sole trader would be paying personal income tax rather than company tax, which would be for registered companies.