I am going on a fact finding trip to Malaga and Alicante, first Malaga and from what I have heard the internet speed is fairly decent, unless you close or in a rural area/in a town surrounded mainly by mountains. I could be wrong but from what I have read Malaga is decent.
In towns, it's generally not a problem, but in the countryside, unless the house has an existing phone Telefonica can be ..... well a better name for them is telefrustration...reticent about giving you a line and despite what you might have been told, they are the only onnes who can install a line. It's pointless asking them if they will agree that they can do it then find excuses or delay for YEARS (this happened to myself and two other people Iknow) the other option is a mobile dongle which might give you up to 3mbs, but that is dependant on the network, their coverage and sometimes even the weather.
Some of the bars are now offering free wifi, before we connected by landline, we did our internet thingy in the bar with our laptop. I would give that a go first, buy a beer or whatever and talk to your Aunty Maude in Melbourne,
Nearly all all towns in Andalucia with a population less than 10,000 have a "Guadalinfo" office which offers a free internet service. This is financed by the Junta de Andalucia and is intended to make the internet more widely available outside big cities. They are used by all ages, from schoolchildren to silver surfers.