Be clear about what this building is before you climb up to it. There has been a stronghold on this rock since Roman times; the Muslim governors held their al-qaṣr here, Alfonso VI and Alfonso X rebuilt it after 1085, and Charles V turned it into a Renaissance palace in the sixteenth century. Then it burned in 1710, burned again under the French in 1810, burned once more in 1887, and in 1936 was besieged for ten weeks and reduced to rubble. What stands today is a reconstruction of the mid-twentieth century, put up by the Franco regime as a monument to that siege. There is essentially no medieval fabric above ground.
The medieval city is underneath. When the museum was extended from 2003 the excavations were kept and incorporated, and the archaeological remains below the building run from the Bronze Age through Roman, Visigothic and Islamic levels — including a Roman cistern about nine metres deep cut into the rock. That is the oldest thing you can stand next to in Toledo, and the museum’s own visitor page lists the archaeological remains among the areas that are free to visit on any day, along with the gardens, the temporary exhibitions and the room “Los ejércitos antes del Ejército” — armies before the Army, which is the pre-modern one.
The ticketed part is the Museo del Ejército, moved here from Madrid in 2010: twenty rooms, a collection above 35,000 objects, arranged both chronologically and by theme. For our purposes the thematic rooms are the point — artillery, flags and standards, firearms, and the arma blanca room of edged weapons. The museum’s own collection page for edged weapons is headed by a Nasrid jineta sword attributed to Boabdil, the last emir of Granada. It does not publish which gallery any given piece is in, so ask at the desk if that is what you came for.
The honest caveats: the great majority of the museum is eighteenth to twentieth century, and the 1936 siege — a founding myth of the Franco regime — is still politically live in Spain and is handled here at length.