Excellent question. Whatever you get, you will end up playing more than your son will. With that budget, you could get a lightly used full motion video game with the top recommendations being Star Wars, Deadpool, and Jurassic Park. If your kid is into Dinosaurs or Star Wars, either would be a no brainer. Another option would be to go with 2 cheaper older machines. Data East Jurassic Park was my 6 year olds favorite (the Dinosaur eats the Ball) and World Cup Soccer was my 8 year olds favorite. You could snag one of these for around $3,000 and have enough left over for a second Alpha Numeric pin like Pinbot or Taxi.
My recommendations would be to either go with Star Wars or Jurassic park (1 nice pin) or to pick 1 DMD (DE Jurassic Park, World Cup Soccer, Gettaway) and 1 DMD (Pinbot, Taxi, Whirlwind). Either way you'll have fun.
Full motion video:
1. Stern Star Wars Pro- 2017 ($4700) Modern game will movie clips. It's star wars. You both can have fun on it. https://pinside.com/pinball/machine/star-wars-stern
2. Deadpool Pro- 2018 ($5000) Great cartoonish feel, no swearing. https://pinside.com/pinball/machine/deadpool-pro
3. Stern Jurassic Park Pro- 2019 ($5200) In contention for best new game of past decade. Kid friendly rules. Just released so hard to snag used ($5800 new).
Dot Matrix Display (DMD)
4. DE Jurassic Park-1993 (~$3200). Very child friendly theme with 3 flippers. The Dinosaur eats the ball! 6 ball multiball. Lots of fun. https://pinside.com/pinball/machine/jurassic-park
5. World Cup Soccer-1994 ($3,000). If you kid likes soccer get this. Simple themes for beginners (shoot goals). Great intermediate goals for average players (light the ramps to lock balls, shoot the scoop to start multiball). Very kid friendly theme with a giant dog on the backglass. https://pinside.com/pinball/machine/world-cup-soccer
6. Gettaway- 1992 ($3000) Fast car themed game with a cool supercharger toy. https://pinside.com/pinball/machine/getaway-high-speed-ii
7. Stern Star Trek Pro-2013 ($4800). More modern game with 3 flippers. Very fast playing game where you can destroy the ship. This is a fantastic pin with some easy modes and a hard to achieve wizard mode. https://pinside.com/pinball/machine/star_trek
8. Whirlwind-1990 ($3000). Fairly simple game that is challenging to master. Shoot the lit shots, hit the ramp to lock a ball, start multiball to start the spinning fan and playfield. https://pinside.com/pinball/machine/whirlwind
9. Taxi - 1988 ($2200). Another fairly simple game that's loads of fun and easy to understand. Pick up passengers and go for jackpots. https://pinside.com/pinball/machine/taxi
10. Pinbot- 1986 ($2000). Kids love this one for the robot. Complete the grid to open the robots visor. Lock balls in visor for multiball. Explore the solar system. https://pinside.com/pinball/machine/pinbot