If you're considering buying a diamond for under $500, you should prioritize which of the 4Cs is most important for you. If you're buying a round diamond center stone for a ring (the most popular and expensive), you might want to prioritize cut over everything else.
An expertly-cut diamond will give off maximum sparkle. But if you want a fancy shape diamond, like a princess or cushion cut, the cut grade doesn't apply. In this case, you will want to think about clarity or even color. If having a larger stone matters to you, then prioritize size.
Another consideration when you buy diamond jewelry (like diamond earrings, diamond necklaces, etc.) under $500 is the metal it's set in. Platinum is the most expensive, while rose gold, yellow gold, and white gold (specifically 14k) are the most affordable.
If you're shopping for an engagement ring and are on a budget, it's best to stay with 14k gold. Sterling silver is less expensive but not recommended for fine jewelry, especially not engagement rings.