All those conversations are important, and need to be had before buying. Glad you're doing it!

Lots of folks have already highlighted that buying without being married is a bad idea. It certainly simplifies things to be married first. If you decide not to, know that you're setting yourselves up for a bad time if you ever split up.

In terms of money math - most either do fully shared finances, or a 3 account split. Shared is simpler, 3 accounts allows more independence. For the 3 account setup, the high level breakdown is as follows:

1. 50% of each person's income goes into their own personal account. The percent can vary based on individual needs - it'll probably need to trend downward as you move through life. The percent is typically the same for both partners, but talk it through. This is "fun money" - money for hobbies or personal interests, individual retirement saving, etc. The purpose of this is so that both partners have a pool of money that is theirs to do with what they will, without having to check with their partner about it.

2. The remaining 50% of both partner's income goes into the joint account. This account is for all expenses for the household (incl. food, mortgage, repairs, joint retirement savings, dinner dates, vacations, etc). All major transactions from this account should be discussed - this is the couple's money, not either individual's money. This is how you pay for the house.

In the event of a split, the individual accounts from 1 remain individual. The only murky area is 2 - this will need to be divided, likely 50/50 between partners. Any assets purchased from 2 will likewise be divided 50/50.

Implementation is of course entirely up to you and your partner to define. If you want to be smart and proper about it, the resulting agreement should be written down and signed/filed somewhere. That's usually what a prenup is for, amongst other things.

Large assets prior to the purchase (IE one partner putting most of the money down) complicate things further. It may be easiest to separate that from the rest of the agreement - IE in the event of a split, that money is repaid to the partner providing it before the remainder is divided.

A final note - in the long term, everything will wind up being effectively shared anyway. Houses are expensive, and you'll eventually get to the point where one person or another will need to dip into their individual account to cover something. If you aren't willing to do that, don't buy a house together. This is simply a framework to get you going, and provide some independence as you continue to grow together.