I'll take the renaissance era to mean 15th and 16th century, especially as you mentioned RPGs which usually get their setting inspired by that period in particular. In some variants Renaissance period covers also the 14th century and even the 17th century, but I won't be mentioning those as the ships then were very different types (although less different in overall sizes).

I also want to first give a warning, while I will offer some numbers on ship sizes given in tons burden (which is suppose to tell how much cargo they could carry) that values are usually estimates (both contemporary and modern) and don't necessarily reflect exactly how much merchant cargo would be carried. Supplies, people, possibly ballast would occupy same part of it, and the ship would not often be completely filled anyway. However it is a okay rough estimate for the cargo capacity.

So, 15th century, cargo size. There were many different types of vessels plying the seas. From sailing ships you had caravel, carracks, older cogs, hulks and round Ships, all sorts of smaller boats. Also rowed galleys, great galleys, fustas, balingers..... The nomenclature is all over the place, especially across different countries and various shipbuilding traditions.

This mess was confusing for contemporaries, and we often see their records simply categorizing ships by size in few different categories. For example, Venetian doge Tommaso Mocenigo in 1423 describes the Venetian fleet as 45 galleys, 300 'Navi' or large ships and 3000 'Navigli' or smaller ships. He doesn't give cargo sizes of those ships, but lists overall crews and says the Navi were manned by 8000 sailors, or 26-27 per ship which historians equal to a 400 botte ship of over 100 (or 200 depending on conversion) tons burden. The 3000 Navigli were smaller ships crewed by 17,000 total, or 6-7 men per ship and were probably mostly smaller ships/boats. The galleys were oared ships and had crews of over 200 men and the larger merchant variants of those would be of 150-250 tons burden size.

Similarly, in a different part of the world, English Bristol custom records for the year 1465/66 recorded three types of ships: "the navis (great ship), the navicula (little ship) and the batella (boat)." The sizes of each are estimated by the cargos recorded in the customs, and Navis is estimated to be a ship of over 150 tons burden, navicula a ship of between 35 and 150 tons, and batellas ship of under 35 tons, a lot of them under 15tons, some as low as 1 tons. The Navis and naviculas were employed as long distance ships to Lisbon, Bordeaux, Spain; while the batellas (with few naviculas) were employed in coastal trade with Ireland.

If we want to map it to some of the known types of ships, we can say that Caravels (in that perios mostly used by Iberians only) which would be ships from 50-70 tons burden and be naviculas for the Bristol customs officer. Carracks were a more common cargo ship, and their sizes could vary a lot. Some could be the size of caravels, or slightly larger, while the huge ones could reach over 1000 tons burden! Those would be incredibly rare, reserved to royal warships or single ships. In the first half of 15th century most larger carracks would fall in 100-400 range, few above 500, which might increase as time go by. Cogs and hulks and round ships of the earlier periods would rarely be above 150 tons, so they would be mostly Naviculas, although some could be large enough to be considered Navis. Galleys (used by Venetians as trade ships in their convoys to Flanders) could carry around 200 tons cargo. Galleys never stopped in Bristol so not sure how they would be classified, but were frequent in Southampton, London and their final destination Flanders.

Just as a last note, I mentioned above that as time went by there was a overall increase in average ship sizes, however that might not be always true. We certainly shouldn't look at it like some linear progression where ships were getting bigger with time. At least it was subjected to various factors. In England for example in the fifteenth century there is a decrease of average sizes of ships which is hard to explain and I personally don't understand completely. Here is a chart that shows that from the known ships in two periods almost 50 years apart, average size of ships decreased and bigger ships almost disappeared. Offered explanations usually list political and military developments but more likely ebbs and flow of economic profitability. A larger ship wasn't necessarily more cost-effective. The problem usually lied in the fact that it longer to fill up a large ship, and harder - a low supply of the product might mean the ship would be half-empty and the voyage not profitable - and it made it's stay in harbor longer which meant later sailings - even sometimes forcing to spend the winter non-sail season abroad - and late arrivals which might mean the demand for the cargo - and price with it - might already be lowered by the ships that arrived before. Smaller ships in that regard could fill up more easily, and more quickly arrive to their destination - and if they are lucky and first - fetch the early, high prices, while the demand is high. they may even try to fit in another run before the sailing season is over. All in all, I just want to stress out that size of ships was a complicated thing and bigger does not mean better or more effective.

To sum up, ships were of varying sizes. For the medium ships 30-50 tons cargo space would be the lower, minimum size. From the larger vessels 100-400 ton size was common, and ships of even over 1000 tons burden appeared occasionally. There were also always a lot of minor ships, but those would be mostly occupied in local trade, not long distance.