Which traders have the most caps available?

While they require an initial investment and the Cap Collector and Local Leader rank 2 to build, the shops you can build at your settlements have quite a lot of caps (between 700-800 for both the level 3 Clinic and level 3 Weapon shop, I assume the other level 3 shops to carry a similar amount.)

The rank 3 of cap collector also allows you to invest 500 caps in a shop once to increase it's buying capacity.

These methods are both reliant on the Cap Collector perks however.

Some Numbers

The Merchants page on Nukapedia has a listing of known merchants with the amount of available caps for most of them. There are a few without a cap amount listed, including notable traders such as Trashcan Carla.

I took that table, and sorted it by caps available. Among those with amounts, most of the wealthiest require the Far Harbor DLC. None of the Nuka-World merchants are listed, at this time.

The wealthiest merchant based on this information is Mitch, in Far Harbor, with 974 caps. The wealthiest without DLC is Doctor Patricia in Covenant, with 748 caps.

I've included that table below, but I've done a little testing myself after first posting this answer, and the numbers don't appear to be accurate. For instance, I visited Mitch twice a few levels apart, found him to have two different values both around 450 caps, and then went and visited Brooks and found him to have just over 700 caps.

Merchant name           Caps    Location                            Requirements
Mitch                   974     Far Harbor at The Last Plank        Far Harbor 
Doctor Patricia         748     Covenant
Brooks                  720     Far Harbor                          Far Harbor 
Sister Mai              698     The Nucleus                         Far Harbor 
Erickson                680     Horizon Flight 1207                 Far Harbor 
Allen Lee               478     Far Harbor                          Far Harbor 
Debby                   469     Far Harbor at The Last Plank        Far Harbor 
Pearl                   434     Vault 118                           Far Harbor 
The Archemist           423     The Nucleus                         Far Harbor 
Kane                    423     The Nucleus                         Far Harbor 
Opal                    417     Rooftops west of Custom House Tower
Slim                    417     Near D.B. Technical High School
Dejen                   408     Acadia                              Far Harbor 
Deb                     390     Bunker Hill
Rachel                  381     Vault 81
Rufus Rubins            359     Goodneighbor
Arturo Rodriguez        352     Diamond City 
Doc Weathers            349     Traveling 
Synth                   347     The Institute   
Trudy                   347     Drumlin Diner   
Supervisor Greene       344     Greygarden  
Rowdy                   343     Atom Cats garage    
Penny Fitzgerald        338     Covenant    
Solomon                 306     Diamond City    
Doctor Sun              304     Diamond City    
Stash                   292     Traveling   
Eleanor                 284     Northwest of Fairline Hill Estates  
Lucas Miller            258     Travelling  
Alexis Combes           254     Vault 81    
June Warwick            253     Warwick homestead                   Minutemen quests 
Moe Cronin              251     Diamond City    
Sheng Kawolski          250     Diamond City    
Fred Allen              244     Goodneighbor  
Myrna                   243     Diamond City Surplus    
Daisy                   242     Goodneighbor    
KL-E-0                  240     Goodneighbor    
Cricket                 239     Traveling   
Scarlett                233     Diamond City    
Brother Ogden           206     Crater of Atom  
Isabel Cruz             200     The Mechanist's lair                Post-Automatron 
Smiling Larry           196     random encounter    
Vadim Bobrov            141     Diamond City    
Polly                   131     Diamond City    
Takahashi               131     Diamond City    
Becky Fallon            128     Diamond City    
Kay                     109     Bunker Hill     
Whitechapel Charlie     109     Goodneighbor    
Bluejay                         Atom Cats garage    
Cog                             Acadia  Far Harbor 
Connie Abernathy                Abernathy farm                      Minutemen quests 
Daniel Finch                    Finch farm                          Minutemen quests 
Doctor Carrington               Railroad HQ     
Kat                             Traveling   
Knight-Captain Cade             The Prydwen  
Leonard Moore                   South of Coastal Cottage    
Maria Summerset                 Vault 81    
Percy                           Diamond City Surplus    
Proctor Teagan                  The Prydwen     
Ronnie Shaw                     The Castle                          Minutemen quests 
Teddy Wright                    Far Harbor                          Far Harbor 
Tinker Tom                      Railroad HQ     
Trashcan Carla                  Traveling   
Wellingham                      Diamond City    

Conclusion

All that being said, CoqPwner is correct in saying that merchants you build have at least as many caps as these options. There's a listing on the Fallout 4 Settlement Objects page at Nukapedia that lists some caps values for the craftable shops, but I'm also quite suspicious regarding these numbers. For instance, it shows the level 3 clothing shop as having 141 caps, but the level 1 as having only 251, which doesn't seem right.

Regardless of how many caps are available at each shop, the best way to sell a bunch of stuff is to go somewhere where there are multiple shops. The Diamond City Market has six (plus the clothing shop which requires loading another cell), which I believe is more than anywhere else. This is probably your first stop for trading for much of the game. Later, when you can build your own shops, you can set up a similar trading hub in any settlement.