@Colin Kanuch apply for the conventional mortgage together and determine how much equity each person will get based on down payment amount. Form an LLC prior to finding a deal with both (all) names in it then draw up an operating agreement spelling out ownership equity between both parties. If your total closing day costs equal $100,000 and you put in $60k and your partner puts in $40k then in your OA you have 60% ownership and partner has 40% ownership. As long as the property is cash flow positive then the closing day is the only time you use your own money. After that it pays for itself. Both names will be on the mortgage equally liable to pay, and then after closing file a quit claim deed with your county into your LLC. I did this exact process with my brother on a STR where I own 65% and he owns 35%. We also setup a joint business account for our LLC that all credits/debits for the property go through. Never our personal accounts. Speak to your lender during the process about the quit claim plan. I have had several mortgages close with my personal name on the mortgage and the title is now in an LLC. It is extremely rare for a lender to call the due on sale clause as long as you keep paying the mortgage. I have asked every lender I've used and the general consensus is, "yeah that's fine, that's what everyone does." Just be up front with them.
Disclaimer: I am not a lawyer, real estate pro, or tax professional. This is just what I have done.
Remember, both parties are equally liable for the mortgage. The bank doesn't care who owes 60%/40% so I would address procedures in case of default in your operating agreement. Any real estate lawyer can put together a solid OA for you to address all these concerns.