Good Morning Chris,
All three forms of financing are effective enough to execute your first, third, or tenth deal so long as the numbers work for your deal. It seems likely most investors would prefer private money, and if you have access to it I would encourage you to consider it. Cash offers make your offers more enticing, will close the quickest, and will allow you to purchase distressed properties that wont qualify for traditional lending. With that being said, using OPM for your first deal might seem a bit intimidating as you are just starting to figure out the ins and outs of the fix and flip business. However, as long as you run your numbers correctly, conservatively, and find that you truly have a good deal on your hands, go for it. Bring the hustle and let your friends and family bring the money.
Hard money isn't as expensive as it used to be. If you factor in your lending costs and still find that you are left with your desired profit margin, hard money is still a considerable option. Hard money lenders are experienced at looking at potential deals and can serve as a second opinion regarding how good of a deal you truly have on your hands. If you're confident that you can complete the rehab within your predetermined time period to keep holding costs from going over budget, hard money can work for you just as well.
Traditional financing could be a road block when it comes to targeting seriously distressed properties, some lenders wont loan on a property that is not in "move in ready" conditions. As a flipper, these properties are the ones that could come with the most opportunity for the bigger profits. However, if you'd like to do a "live in flip", traditional financing can be a viable option for you.
Look at your investing three dimensionally, with more experience and resources you will find that one day you are actually utilizing all three forms of financing to fund your business as you take on more rehabs throughout the course of your investing career.
Good luck, keep bringing the hustle!