Pneumatic tires are a good option when you want to drive around the cart on sand. A pair will set you back by roughly $30. Also, they are easily available on amazon. The DIameter of 10 inches is a good choice to go with. There are numerous such tires available on amazon with different dimensions.

Many of the top beach carts also use such tires. As for driving around on sand, unless you get larger wheels, wet sand will require more effort. Unfortunately, the larger ones also cost more. However, on dry sand, these pneumatic tires work great. Before you make your final decision, it is a good idea to take into account a few factors:
- Diameter
- Load carrying capacity
- Construction material
Your budget is more than enough in a nutshell and also, pneumatic ones can provide you with proper traction on dry sand as well.