The most prominent personal weapon would be what's now called an arming sword, a double-edged sword meant to be used in one hand, straight-bladed and tapered to a point. This kind of sword is found throughout period all throughout the medieval period, extending centuries on either side of the 13th centuries. This was overwhelmingly used with either a full shield (represented in battle scenes) or a buckler (represented in cases of personal combat and attested as the main equipment for travellers and other common folk). In addition, the long knives that people carried with them as a part of day-to-day life (about a foot long, either single- or double-edged) would be omnipresent. There are also various versions of falchions (single-handed single-edged blades, often but not necessarily curved) either as dedicated weapons or the use in combat of machetes that would be a common tool in daily life. There is also a range of maces, clubs, axes, and similar weapons to be found in the pictorial and material record.

Military weapons would have these swords and knives and whatnot as sidearms, with polearms of a dizzying variety being the main hand-to-hand weapons (spears, pole-axes, halberds, pikes, bills, etc.). We also have illustrations on the Courtrai chest from the start of the 14th century (representing the Battle of Golden Spurs in 1302) where many of the Flemish townfolk are using clubs ringed with spikes an addition to polearms and falchions. Shields seem much more common than bucklers in the military context, whereas bucklers predominate in personal combat and polearms (except for quarterstaves and the like) being basically absent. This is easy to understand because polearms and shields are extremely effective on the battle field but can hardly be something you could carry around in civilian life (not just because they're big and clunky, but also because it would be like walking around with an assault rifle). Quarterstaves and bills you could perhaps get away with because they were also features of common life (bills are agricultural tools, staves are just staves) but they are still extremely cumbersome to always have around.

This is easy to answer because we have ample pictorial evidence from this period of what especially the noble and knightly classes of Western Europeans would be using in combat by way of, for instance, the Morgan Bible and the Codex Manesse. The late 13th and early 14th century is also when fencing manuals start appearing, with the very earliest one (the so-called Walpurgis Fechtbuch coming around 1300 (maybe slightly later), which describes combat with a sword and buckler. The pictorial evidence overwhelmingly represents nobles and knights, but also extends to general men at arms and travellers. For instance, the Walpurgis Fechtbuch is written by monks (possible retired mercenaries, but there's no real way to know) and doesn't seem to be a portrayal of courtly figures. We also have accounts from the Canterbury Tales from the 14th century, for instance, describing pilgrims as arming themselves with sword and buckler, which seems to be a long-established practice.