Background
My partner and I (not married, but together for years and in it for the long-term) both share many of the same goals and all of the same criteria for wanting to own a home. It's worth noting that our options are a little limited (at least where we find ourselves geographically), because we have fairly picky criteria. The home criteria is based on shared interests/hobbies, e.g. wanting a good yard for gardening. We're not so interested in moving as I have a good job where we are and my partner just finished school and has a good network in the area, an area we both like and have some roots in.
My partner is most interested in buying a home in order to build equity, as they grew up elsewhere and don't have much family, property, or funds to their name. I'm interested in owning a home for the reason of building equity as well, simply because my main passion/hobby is more feasible and beneficial when owning vs. renting (e.g. trees grow, landscape gets nicer over time).
We've been looking at homes and have started to see some promising ones. My partner was waiting to find stable work before trying to get pre-approved for a loan, but finding good options and in the off-season, there's more motivation to go get pre-approved sooner than later in order to start the process of making an offer, having a home inspection, etc. My partner has earned income while in school through various skilled (as in, requiring their qualifications) part-time and seasonal jobs. They have a history of success and as a hard-worker, but in field that doesn't pay the greatest and has limited job opportunities (existant, but scarce and cometitive) - having worked a lot in another country also contributes to their starting off with relatively little. I have verified some of their past work, have seen their current, and trust them.
That leads to the question:
What are the methods available for us to buy a home and which is recommended or not, for what reasons?
For example:
Option 1: we could apply for a mortgage together, buy together unmarried and be both 100% liable for the loan yet with split ownership and a legal contract to handle potential complications.
Option 2: My partner could go through the buying process solo, and I pay rent as a tenant living there. Improvements I make to the home would potentially end up as a gift to them if we split and I had no ownership, but I am better off financially to begin with and the home improvements I'd contribute to wouldn't be anything I couldn't happily 'gift' and walk away from (or if they were, I'd arrange a fair deal for that).
Option 3: I could buy the home on my own and allow my partner to 'rent to buy' in some way. This may be valuable if my partner's less ideal financial situation proves to be troublesome in securing a suitable mortgage, but it is also not ideal in that it may keep my partner from having the sense of home ownership and stability they're after. I realize there are risks with this, but I think most of them are less critical when considering that I would be happy to commit to buying this home on my own. It is a home I'd enjoy, it is rentable, it is sellable.
Additional considerations:
My partner, having legally migrated from far away years ago, has more reason for wanting to own (building more tangible roots and some equity), and so it makes more sense for them to at least have some ownership and not have me take on all ownership.
I have more funds, a stable job, and am younger. This could make it easier for us to get a mortgage if I get involved, but at what benefit and risk to us as partners and as individuals?
If co-owning is too complicated, the default would be for them to proceed as an individual. This may even be preferable, to ensure they get the sense of ownership that is an important part of the purchase to them.
Setting is upstate NY, USA.
Some local home info: looking on the more frugal, practical side; rentable and sellable due to the location and types of homes we're looking at. Price-to-rent ratio is at best ~8 and at worst ~13, in an area with multiple universities where we can find housemates, or can rent or sell if we move out.