Bill_of_the_Midwest:
So please help me. Is my project simple enough to just use delay?
Is there a reason not to?
Yes, if you are just getting started then the project you describe is a good use of delay. As already mentioned, the major drawback of delay is that you can't do anything else while delaying. (Even that isn't entirely true.)
Take your plan and implement it. There's no substitute for the experience of learning. Just know that later on if you want to start doing multiple things or doing more during your "delays" then you'll need to make some changes.
Also, since you are using relays, make sure you read tutorials on them. You can't just drive a tutorial directly from an arduino I/O pin.