To find out how many complete uniforms the coach can buy with an $800 budget, we need to divide the total budget by the cost of one uniform.
The cost of one uniform is $23.99. Therefore, we calculate:
\[ \text{Number of uniforms} = \frac{\text{Total budget}}{\text{Cost per uniform}} = \frac{800}{23.99} \]
Now we perform the division:
\[ \frac{800}{23.99} \approx 33.34 \]
Since the coach cannot buy a fraction of a uniform, we take the whole number part of the result. Thus, he can buy:
\[ \text{Number of uniforms} = 33 \]
To confirm this, we can calculate the total cost for 33 uniforms:
\[ 33 \times 23.99 = 789.67 \]
This amount is within the budget. Checking for 34 uniforms:
\[ 34 \times 23.99 = 815.66 \]
This exceeds the budget of $800.
Therefore, the maximum number of complete uniforms the coach can buy is
\[ \boxed{33} \]