@Brent Perkins You are where I was when I started investing in real estate. I did a cash out refi and then retained the house as a rental, and I still believe in that decision.
At the end of the day, it comes down to opportunity cost. If you sold that house and took the cash, what would you do with it. Invest it? Invest it how?
If you believe that the stock market is a better place for your money than real estate investing is, then go for it. You won't find much of that opinion on this website, but that's your prerogative. You won't have $100k to invest, though. Selling a house costs you about 6% of its value in agent commissions. For a $240k house, that's ~$15k lost forever.
But if you believe in real estate as an investment, then you need to understand that transaction costs are huge in real estate. Selling will cost you that $15k, and buying costs you a good $5k in closing costs. In other words, if you sell your house and use the money to buy a different house as an investment, your transaction costs will take a huge bite out of your money!
Far better is to choose a different tax-free option: not selling. Obtain your first investment property without the costs of an extra sale OR an extra purchase - just repurpose the house you're moving out of! You'll have some combination of monthly cash flow, mortgage principal payments, and house appreciation all adding to your net worth. The rate of return on your equity is usually far larger than you could expect to earn investing that money in other ways.
In fact, many investors deliberately move every few years just so they can purchase using friendly owner-occupant mortgages, improve the property while occupying, and add to their portfolio by moving out.
Now, what about selling? Won't that big tax bill come eventually? Not necessarily. You can use cash-out refinances to extract more equity forever. Why ever sell, as long as the investment is worth it? Own 'til you die!
None of this means you get out of having to do market analysis, though. It may be that your current residence makes a uniquely terrible rental. Your suggested $500/month cash flow sounds good, but that's pre-refinance. I also have no idea whether you ran your numbers correctly, or whether your neighborhood is growing or dying.
What I am saying is that the fact that you already own it is a huge benefit vs having to buy to invest.