This
https://www.jameco.com/webapp/wcs/stores/servlet/Product_10001_10001_120539_-1 kit has a slight amount of soft-start available. I used it to drive a shutter. It is noticeable, but I don;t know the time frame.
If nothing else it gives you speed control out of the box and it might be able to set two speeds using two pots and a slight circuit modification.
If you implement dynamic braking, you can have fast stops. One method is to short the motor when commanded to stop.
"H-bridges" like the L298 is available in many kits. They can reverse and drive the motor directly.
Usually they use Direction and "Not enable" as control signals. A carryover to when TTL floated high.
Some drivers offer coast, brake, fwd and reverse.
Any method you choose will have it's own constraints and upgrade paths.
I'd suggest looking at
www.picaxe.com. So, this
https://www.canakit.com/catalogsearch/result/?q=uk1122&x=0&y=0 and a PICaxe, a logic supply and some glue logic.
Reversing can be done with a single relay as well, so the PWM kit and it's built-in soft start can become a start.
You can modify the PWM kit to drive the H-bridge. So, now Analog control (0-5V) can be used to control speed.
Later, you can use use the PICAXE to both control speed, acceleration and direction to the L298 driver.