Short story, the "most classic" [1] is to use the .4% DB=>MWB for coolng and .4% Condns DB for heating which corresponds to the hottest and coldest months respectively (with highest/coldest dry bulb temperature).
Obviously the other types of design days have value too, depending on the equipment/application you have. Cooling design days based on wetbulb are useful for sizing cooling towers for example. Below I've tried to summarize which design days are useful for which application.
Cooling:
DB=>MWB: Chillers and air conditionnersCondns WB=> MDB: Cooling Towers and other evaporative coolersDP=>MDB: These values are especially useful for humidity control applications, such as desiccant cooling and dehumidification, cooling-based dehumidification, and fresh-air ventilation systemsCondns Enth=>MDB: this is used for calculating cooling loads caused by infiltration and/or ventilation into buildings. Enthalpy represents the total heat content of air (the sum of its sensible and latent energies)
Heating:
Condns DB: General heating applicationsCondns DP=>MCDB: to size equipment for humidification applications.Condns WS=>MCDB: Wind design data provide information for estimating peak loads accounting for infiltration
References:
All above information is based on Chapter 14 of the 2009 ASHRAE Handbook of Fundamental.
There are newer sources in the ASHRAE HoF 2013, and the resulting EnergyPlus .ddy here
[1] From ASHRAE HoF 2009:
Annual Heating and Humidification Design Conditions.
The month with the lowest mean dry-bulb temperature is used, for example, to determine the time of year where the maximum heating load occurs.
The 99.6 and 99.0% design conditions are often used in sizing heating equipment.
Annual Cooling, Dehumidification, and Enthalpy Design Conditions.
[...] The 0.4, 1.0, and 2.0% dry-bulb temperatures and mean coincident wet-bulb temperatures often represent conditions on hot, mostly sunny days. These are often used in sizing cooling equipment such as chillers or air-conditioning units.
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Matt, I took the liberty of editing your post to include the picture directly in there and removing the greetings as per our convention.
Great to have you on board though, and tanks for the encouraging words :)
Also, considering this is actually not an OpenStudio specific question, I'd tend to rename it to something like "Which design days do I need for sizing purposes". What do you think?