The quick-play buttons on tf2 start menu can be a bit deceiving since it ranks some gamemodes higher on the list versus others, it doesn't necessarily dictate actual popularity or desire for the gamemode.
If it helps at all for your decision making process. I created a saturation ranking based on the gamemode, amount of servers available, and amount of people who play that particular gamemode, this only counts valve based map rotation servers not custom maps. I picked up this data over a one week period measured every 60 minutes to calculate the average. The intent of these calculations was to figure out what quickplay people really enjoy playing. I did this a while ago, just happen to find it in one of my old google documents, but for the most part this has always been true for TF2. You only see slight variations when a new map is released in a patch. I could go into detail what the number you see below exactly means but essentially to keep it simple, the higher the value the better, meaning the larger the quickplay population pool that is available and the higher demand for such a server. I never did this calculation for arena unfortunately, also I did this calculation based on 24 slot servers only. 32 player servers are not factored into quickplay beyond 24 slots unless the demand for 24 slot servers is met or exceeded which rarely happens during patch days.
Payload Average Value: 134.76
Attack/Defend Average Value: 60.12
CTF Average Value: 120.55
Koth Average Value: 34.43
CP5 Average Value: 22.76
goodluck on your decision!