Devils Advocate here:
If the market value of the home is $250k and you are buying at $220k, the initial equity capture is attractive. However, you are doing a BRRRR, which assumes there will need to be rehab. What is the cost of that?
Further, your post doesn't go into rental rates. Very important because, while principle pay down is awesome, the asset should produce income. It needs to cash flow.
With the aforementioned questions, you have discussed financing. There's two levels of financing on the deals I do - the first level is the one that takes care of initial purchase price and rehab budget. You cash use cash, hard money or private investors to do this…I think private money is easiest to work with. The second level is once the home is rehabbed and leased. Your refinance it into a conventional loan.
To each their own on the conventional loan. However, I would always do a 30-year. If you've got a 30-year, then you can make it a 15-year, but you can't make a 15-year a 30-year. The covid situation and the eviction moratorium is a great example of this. What happens when your tenant doesn't pay and you can't kick them out?! You'll want the lower overall payment.
I'm not an expert. I hope some of this helps. I have done 4 BRRRRs, and I have 2 under contract. Happy to answer any questions to the best of my ability.