[lathspell]

A few notices.

The oldest elf is indeed Cirdan the Shipwright. He was among those few Elves that lived in Darkness before they were brought to Valinor by Oromë. I don't know wether he was a first-born elf, but he was definitely among them when their great journey began.

Oldest person is quite another thing. Huge threads have been given to this matter. Personally I'm inclined to think Bombadil is indeed oldest. I have a few reasons:
1. Goldberry says so in LotR: 'Eldest, that's what he is!' This assumes that he was older than her (I always thought of Bombadil's finding Goldberry near the river was a kind of metaphor for her birthing, so that would be another reason). Since she said it, and I think it safe to presume that she knows her mother's age, it would be safe to assume that he is older.
Than there is the point were speculation comes in. We don't know anything about Goldberry's mother. For all we know she disappeared or died. Calculations are not possible without further information on her part.

2. Tom Bombadil must be older than Treebeard, him being the Eldest Ent. In the Silmarillion Manwë says to Yavanna: 'When the thoughts of Iluvatar come alive, so also will the thoughts of Yavanna!' This after the Great Song and the Valar coming into Arda. Bombadil claims to have been her ever since the Great Dark Lord came from Outside when the world was ever dark. Bombadil saw the Valar come, therefore he was oldest.

Hoping this topic will never burn out,
greetings,
lathspell