Hello mlazenby! Welcome to our forum!
I agree with Tony about the indispensiblity of a laptop computer. Just for English teaching alone it has so many uses. In fact, I started
THIS THREAD a while back soliciting input from other teachers out there. You might want to take a look at it. If you are going to be teaching English, I highly recommend that you bring a laptop computer. If you are lucky enough, the flat that you will be living in will have an internet connection. Many consulting agencies and academies do not give you materials to use, or very minimal resources, so there is always a wealth of information available on the internet to enhance your teaching. Better to have your own computer than to wait in line at an internet café (locutorio) and pay high prices, or hope that the place that you work for has one.
There are various places throughout Madrid that offer free WIFI connections. Check out
this discussion thread for a list of free places in Madrid. There are also several
cheap internet cafés in the center of Madrid if you happen to live in that area.
I firmly believe that an internet connection for expats in this day and age is an absolute must have. I keep in contact with my friends and family around the world through the internet and it sure as heck saves on the phone bills!
Even better, if your laptop has a DVD or CD recorder it's a great way to organize your teaching materials and have a permanent record of your lesson plans that you can recycle with your different clients.