Calculate the fees for different ATM and teller withdrawal scenarios.

The fee structure for a Denbank ATM is R3.50 plus R1.10 per R100 or part thereof.

• Withdrawal amount: R1 000
• Number of R100 blocks: $\frac{\text{R}1000}{\text{R}100} = 10$
• Fee = Base fee + (Number of R100 blocks $\times$ Fee per R100 block) $$\text{Fee} = \text{R}3.50 + (10 \times \text{R}1.10) = \text{R}3.50 + \text{R}11.00 = \text{R}14.50$$

The fee charged is $\boxed{\text{R}14.50}$.

The fee structure for another bank's ATM is R5.50 plus R1.10 per R100 or part thereof.

• Withdrawal amount: R250
• Number of R100 blocks (or part thereof): $\lceil \frac{\text{R}250}{\text{R}100} \rceil = \lceil 2.5 \rceil = 3$
• Fee = Base fee + (Number of R100 blocks $\times$ Fee per R100 block) $$\text{Fee} = \text{R}5.50 + (3 \times \text{R}1.10) = \text{R}5.50 + \text{R}3.30 = \text{R}8.80$$

The fee charged is $\boxed{\text{R}8.80}$.

The fee structure for "Over the counter" (teller at a branch) is R23.00 plus R1.10 per R100 or part thereof.

• Withdrawal amount: R250
• Number of R100 blocks (or part thereof): $\lceil \frac{\text{R}250}{\text{R}100} \rceil = \lceil 2.5 \rceil = 3$
• Fee = Base fee + (Number of R100 blocks $\times$ Fee per R100 block) $$\text{Fee} = \text{R}23.00 + (3 \times \text{R}1.10) = \text{R}23.00 + \text{R}3.30 = \text{R}26.30$$

The fee charged is $\boxed{\text{R}26.30}$.

• Withdrawal amount: R250
• Fee charged (from Step 3): R26.30
• Percentage = $\frac{\text{Fee}}{\text{Withdrawal amount}} \times 100\%$ $$\text{Percentage} = \frac{\text{R}26.30}{\text{R}250.00} \times 100\% = 0.1052 \times 100\% = 10.52\%$$

The percentage charged in fees is $\boxed{10.52\%}$.

The fee structure for a Denbank ATM is R3.50 plus R1.10 per R100 or part thereof.

• Withdrawal amount: R600
• Number of R100 blocks: $\frac{\text{R}600}{\text{R}100} = 6$
• Fee = Base fee + (Number of R100 blocks $\times$ Fee per R100 block) $$\text{Fee} = \text{R}3.50 + (6 \times \text{R}1.10) = \text{R}3.50 + \text{R}6.60 = \text{R}10.10$$

The fee charged is $\boxed{\text{R}10.10}$.

We need to compare three options for withdrawing R250:

• At the bank (Over the counter): From Step 3, the fee is $\text{R}26.30$.
• From Denbank ATM:
  • Withdrawal amount: R250
  • Number of R100 blocks (or part thereof): $\lceil \frac{\text{R}250}{\text{R}100} \rceil = 3$
  • Fee = $\text{R}3.50 + (3 \times \text{R}1.10) = \text{R}3.50 + \text{R}3.30 = \text{R}6.80$
• From a tillpoint with a purchase: The fee is R5.50 per transaction, regardless of the amount withdrawn. $$\text{Fee} = \text{R}5.50$$

Comparing the fees:

• At the bank: R26.30
• Denbank ATM: R6.80
• Tillpoint with a purchase: R5.50

The lowest fee is R5.50.
It would be more cost-effective to withdraw R250 from a $\boxed{\text{tillpoint with a purchase}}$.