1994 Honda Accord won't start when only turned off for a few minutes. I have to wait 10 minutes and then it starts. What could this be?

This problem has been going on for over a year now, and I haven't had the money to fix it. I
first noticed it at gas stations. I'd stop, turn off my car, fill up, and then the car wouldn't start.
It might turn over a bit but doesn't start. If I wait 5-10 minutes, it'll start. I've also found (and
I'm not sure if this is true but it's just a guess) that if I hit my gas pedal right as I turn the key,
then it might turn on for me. It doesn't always work though. I'm hoping someone here can tell
me the problem so that I can get an idea of how much it'll cost me. The car is very old and
has many other problems but this is the most debilitating. I don't want to sink thousands into
a car worth less than $500 but I do need it for work. Thank you to anyone who can help!

P.S. if there are multiple options, feel free to give me a list and I can figure out what might be
possible for me to fix given my budget.