If I am putting in half of the money for the down payment,
and paying half of the mortgage, what claim do I have to the property if we
split up before the marriage or divorce at some point down the road.
I'm not a lawyer and wouldn't want you to rely on what I say, but here are some thoughts:
It is probably sufficient protection for you (but not her) if you have the deed in both names. It's possible that the lender might not be OK with that - they may want all owners to sign the mortgage. You'd want to check that before you actually make an offer on a house.
If your fiance is the only one "on the hook" to pay the mortgage, putting the deed in both your names might not be the best protection for HER. If you split before the wedding and stop paying towards the mortgage, she will be left having to pay the full mortgage on a house she only half-owns. Ditto if you stop paying your share at any later date.
A better option would be to get married before you buy the house. Probably you could get legally married without a big ceremony now, and then repeat your vows later at the wedding celebration you are now planning to have.
You'd want to check this out with a lawyer, but I think that if both the house and the mortgage are acquired during the marriage, they'd both be community property in a divorce (even though the lender can only sue her, not you, for defaulted payments, the divorce court would count both the unpaid mortgage balance and the house's value in the community assets to be split equally). If I'm wrong about that, then it might be fairest to bite the bullet and put both names on the mortgage as well as the deed.
A third idea to consider would be for you to sign a mortgage to her. First she buys the house in her name and signs the mortgage from the bank. Then after the dust settles and you're ready, you sign a mortgage with your fiance as the lender, for half the amount owed to the bank, and in return at the same time your fiance would sign a new deed putting the house in both your names. You'd then go and record both those documents in the county property records. But before you do that you should probably check whether it would violate the terms of her mortgage from the bank, just to make sure.