I have a 25 GAL tank on my compressor. I can tell you that it is just enough when I start with a pressure of 125 PSI on the tank.
There is a big difference between $18 and $85 but in the long run you'll thank yourself for buying it. However if $85 is just way out of your budget, I have 2 kids under the age of 5 so belive me I understand how tight money for the big kid toys can be. Go ahead and get a 5 Gal tank until you've got the cash to upgrade. My brother had a setup like the one you're describing that he fills at home with a $25 compressor he bought a Lowes. It works OK but he spends more time rechaging it than actually using it.