I would recommend that you start with an Arduino. There are Arduino Nano clones for less than $2, free shipping on eBay, with USB serial port integrated and they are faster than the usual PIC16/18, even when programmed in C. But if you want, you can actually use the underlying registers with it, no need to use the Arduino API. I use it frequently when I test things like new displays, sensors etc., or even for bigger projects, like this "bateye" hardware which I wrote for someone on Hackaday:
https://github.com/DebarghaG/Project_Basics/blob/master/bateye-stereo.inoIt uses two ultrasonic distance sensors and creates two audio signals, depending on the distance, logarithmically scaled (bigger frequency steps with higher frequencies, because the ear perceives this as linear then). I had to configure the Atmel registers myself for the interrupt, because this is not possible with the standard API (but there is a timer1 module for it, as I just found out), but the rest is really easy with it.
When I need more power, currently I use one of the STM32 microcontrollers. The CubeMX GUI makes it very easy to configure all peripherals, you really don't want to do this by hand. The code looks horribly bloated, but it has big enough flash memory, so I don't care, and they improve it all the time, it has fewer and fewer bugs with every version
I use it in combination with the Keil uVision IDE (free for up to 32 kB).
Some bigger STM32 chips run with 168 MHz (costs like $10), the smaller ones with 48 MHz (for like $5). But it is still simple enough with one supply voltage and internal oscillator, so you can use a breakout board and start playing with it (with a ST-Link programmer, which is again cheap on eBay). I used this to test a new 3-color e-paper display:
https://hackaday.io/project/20466-wifi-epaper/log/61762-stm32l433-and-new-display-testLater I created a proper board, which is currently manufactured:
https://hackaday.io/project/20466-wifi-epaper/log/61807-test-board-for-bluetooth