Disclaimer: I am an attorney, but I am not your attorney. This is not legal advice, just friendly information.
Typically, and LLC is an easier vehicle to navigate since it includes the liability protections, plus outlines the agreement between the partners. Keep in mind that the LLC will need to be registered to do business in CA and pay that fee, even if it owns the home and does everything in the other state.
Changing from partnership (or TIC) to LLC and reverse should not have tax ramifications, since the IRS disregards LLCs anyway and considers it a partnership. If the LLC changes to corporate taxation, that will be a change. If you want to move the LLC or change it later, that will depend on the states involved (whether it can be domestication or conversion, which is way beyond this forum post).
If the financing is a necessary piece, then at minimum there should be a comprehensive partnership agreement. A partnership can still be useful, and you could get a DBA for banking purposes.
In my experience, a "simple" business relationship is best done with a detailed "complex" partnership or LLC agreement. That's because a strong agreement outlines the various problems and provides solutions up front. Got a problem? Check the agreement for the solution.
Conversely, a simple agreement leads to a complex relationship, because each time something happens, the parties need to sort it out, which leads to new disagreements. You'll end up spending time coming up with solutions, rather than focusing on making money.