I'd start by taking off a rear wheel and assessing if your ride on is slow due to slow gear boxes. It also helps to look at the original packaging or an ad that will tell you what MPH that ride on was built to achieve. You'd need to pull the rear tire off to see what your current gearbox adapters look like. Alot of these come with a 9k rpm setup (it'll be on the motor). Bumping up to 15k -30k rpm gearboxes will net your more speed with little effort.
I'm a big fan of simplicity and I generally advise to get rid of parental remote boards as soon as possible. The board adds a degree of complexity that in my opinion makes the toy unreliable and also hinders future speed upgrades.
For example your controller may take 18v for alittle while but it will eventually fail, sometimes it's the first day, sometimes its a few months. A 24v Board may work undervolted or it may fail.
Usually my course of action is to graft a wiring harness, switches, and pedal from a donor like a dune racer, f150, Power wheels jeep, or others that don't utilize a controller. This allows you to go 18v-20v easily and reliably.
A 30-40AMP fuse at the battery before any other components is generally a good idea to prevent fires or overheating. A Thermal fuse will reset when it gets too hot, or a blade style fuse will just pop like one in your automobile. Example - https://www.amazon.com/MCIGICM-Inline-Fuse-Holder-Blade/dp/B081DHT8Y7/ref=sr_1_5?dchild=1&keywords=fuse+holder&qid=1627995819&sr=8-5
Drill batteries in my opinion are great and irritating. They give you easy battery swap and decent power. However they are usually low AH ratings (low run time) and require another component (LVC) and a relay to prevent overdischage. LVC's, Relays, Control boards are again another degree of complexity that I don't like. But your mileage may vary.
I wouldn't start with an ESC right out of the gate, as it involves more components and effort