I plan on using ARDUINO, but what arduino should i use?
You have some inputs. Each coin slot needs some sensor to detect when a coin passes by. Three slots == three sensors.
You mention a keypad. That takes some pins. How many depends on the unspecified keypad.
You have some outputs. There is text on an LCD. The unspecified LCD needs some Arduino pins.
You need some way of ejecting coins. Three slots == three output devices.
Add up all the pins needed. Determine which Arduino style (there's really only two) has that number of pins.