Arduino UNO with CD4510 Counter
The CD4510 does not seem at all appropriate for this task. It is a counter chip that counts up or down. You can do that with the Arduino. The output (of the CD4510) would be in "binary" and not suitable for driving a 7-segment display.

You can get 8 digit 7-segment displays on eBay for around $2. Surely that fits within your budget?