Sale vs Rent

Sell to harvest the tax exclusion and use to put 20% down on the next house.

If you lived in the house for at least two years and sell it within the next three years you can take advantage of the home sale cap gains tax exclusion of $500K (MFJ) or $250K (Single). You will also start the clock on your next home sale tax exclusion period. If instead, you rent out the first home indefinitely, you wil get to depreciate it and can take advantage of a 1031 exchange when you sell it but eventually you will have to pay the full cap gains tax (unless you die first).

I like locking in the tax break while it is available.

Realistically, a good rule of thumb is to expect 50% of the rent revenue to go for expenses. So, that leaves you with gross rent of approximately $42k ($3500 x 12), and net rent of $21k (half of that) per year. And I want to point out that you don't mention what the current mortgage payment is, so odds are that depending on your current payment the cash flow might actually be near zero (or even negative).

Compare that with an alternative of selling the house and putting the proceeds into an index fund or ETF (S&P500). If you sell the house for $700k, then lets say after it's all done with you walk away with $550k (that's $700k, less $125k to pay off the mortgate and $25k for other transaction costs). If you wanted to use a typical conservative "8% stock market return per year" then year one would see that investment grow by $44k.

Of course, the stock market is much more volatile than real estate rental. So next year might another year of 25% return in the stock market, or it might be down 25%. So, you have to ask yourself what your goal is. If the goal is to invest for the long term and to maximize the return, then keeping the house as a rental is probably not the right approach. If you want to hang to the house because you think you might go back to that area or because you might want to pass it down to someone in the family, then it might be worth keeping and renting it out.

But, based on the numbers you've given if I were in your shoes I would sell the house without a second thought.