Iron is your best bet for armor and weapons when starting out in Going Medieval, and it's also needed for other items. That being said, you can get iron quickly by mining it from iron ore veins, as shown above.
However, before you can turn the iron into useable material, you must research the technology smelting from the tech tree. To do this, you will need a research table placed and enough books to get to the smelting on the tech tree, which will be about 45.
That said, to get this amount of books, simply start a production inside the research table for 45 books and set your smartest settler (the one with high intelligence) to research. If you don't know how to do this, just go into jobs and find them under the listing and change the research job to priority one.
After this, your settler should start pumping out books in no time, thus allowing you to unlock all of the necessary tech trees. Once done researching, you can then build a smelting furnace with 70 limestones to produce iron ingots.
To get the limestone bricks you need for the furnace, you will need to mine limestone deposits, research stone block cutting, and build a stone mason's bench with 60 wood.