How are you completely unaware of all of this?
Rings aren't mandatory for an engagement or to get married. Therefore the short answer is, do absolutely whatever you want to do.
The long answer - obviously taking into account that "tradition" is not a law or an expectation, not all couples are male-female, not everyone wears a ring, and again you're allowed to do anything you want in regards to rings:
- "Traditionally," the man presents the woman with a diamond engagement ring when he proposes to her, as a symbol of the engagement agreement they've just made.
- "Traditionally," the couple exchanges gold wedding rings during the wedding ceremony as a symbol of the marriage vows they've just made to each other.
All that being said:
- Some engagement rings do not contain diamonds - they instead use colorful gemstones (sapphire, ruby, etc.), artificial/lab-made diamonds, or no stones at all.
- Some women choose to wear just one ring to symbolize both the engagement and the wedding vows, rather than two separate rings.
- Some men choose to wear an engagement ring.
- Some men, and some women, choose not to wear a wedding ring.
- Weddings rings may be made of a metal other than gold, such as platinum or palladium or titanium. Or even an alternative material such as wood.
- Some people don't have just one dedicated engagement/wedding ring. They may have multiple rings (either fine jewelry or fashion jewelry) that they switch around to coordinate with their outfits.
- Some people choose a symbol other than a ring to symbolize their engagement or wedding - watch, earrings, necklace, bracelet, or a non-jewelry item like a tattoo.