Since nearly any I/O pins of todays FPGAs can be used for a 200kHz PWM it is more the question what you define as an "easy to use" FPGA.
In the link attached you find an example project based on an Altera SoC-FPGA. Depending on your application the device is maybe oversized but it should give you an idea. Also the project uses only one PWM channel but the shown PWM controller can be instantiated 16 times.
For 16 channels even a bigger CPLD might suffice... Almost any pin of the PLD device can be used for your needs. I'd suggest you to use Altera DE0 Nano (http://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=English&No=593) or Digilent CMod S6 (Xilinx Spartan 6) (http://store.digilentinc.com/cmod-s6-breadboardable-spartan-6-fpga-module/) or Digilent Basys 3 (Xilinx Spartan 3E) (http://store.digilentinc.com/basys-2-spartan-3e-fpga-trainer-board-limited-time-see-basys-3/). I think Arty can also do well but can be a bit complex for the task.
What do you mean by "easy to use"? Coding with HDL is the same for all devices.