Broadband internet is typically charged not by speed, but by the amount of foreign data you download. For DSL, prices on Vodafone range from about 4000 for a 10 GB cap to about 7500 for 140 GB. Or you can get a much faster fiber optic connection with the same data caps. The fiber plans are actually cheaper as far as Vodafone says, but you also have to pay a fee to the company who owns the fiber lines, so it ends up being maybe 1500 ISK more expensive to have fiber.
From 200.000 ISK, you'll bring home somewhere around 140.000 (assuming I have an accurate understanding of the tax code here).
Is that enough? It's always very hard to answer this sort of question, because so much depends on your expectations for your standard of living. What's plenty of money for one person might be catastrophically low for another. If you start with 140.000 ISK after taxes, plan to spend at least half that on food. Even if you cook your own meals at home and bring your own lunch every day, it would be hard to shrink your food costs to much below 70.000 ISK a month I think. If your rent and utilities are paid, then you can start to figure out whether the money left over would allow you to do the things you want to do.
Surviving Iceland
