While I agree with your caution about becoming house-poor, simple business logic should make it clear that you can't rent a similar home for less than the costs of ownership.
This because the landlord is running a business, not a charity, so he'll pass along to you his costs, plus the principal part of his mortgage payments, plus enough profit to make it worth his while. If you were the owner, the principal portion would be increasing your own net worth rather than the landlord's (of course it could be a landlady, but the effect on your finances would be the same).
You can, of course, rent a cheaper place than you'd buy, but if that's the case, you're comparing apples to oranges - both are fruit, but different ones.
As for appreciation, that's sort of a hit or miss situation. To date I bought three homes. Two appreciated 9-13%/year after adjusting for inflation, while the last lost ~1.7%/year after adjusting for inflation and a remodel.
On average, over the long term, residential real estate appreciates about 1% faster than inflation. This is much less than the 6-7% real return on stocks or even the 2-3% real return on bonds. However, if you put 20% down, you significantly accelerate your return on your house.
For example, say you pay a $80k down payment on a $400k home. In normal times, with 3% inflation, your house appreciates by ~4% and after a year is worth $416k. Your equity went up by $16k, or about 20%. Adjusting for inflation, that's a 17% real return. Even better, the dollars you owe on the mortgage principal are worth 3% less, and your interest rate, which might have been 3.5%, after the tax benefit, costs you about 2.4%, which is less than the 3% inflation.
Bottom line, as I explain in detail here: https://medium.com/financial-strategy/if-youre-renting-your-home-you-need-to-see-this-1dd55f06dfa in most cases where you can afford the down payment without making yourself house poor, have stable income, and aren't planning to move in the next few years, you'd be far better off financially to buy than rent the same kind of place.
If you can't afford the mortgage payments, you probably can't afford to rent something like it either (unless you've been renting it for a while and it's rent-controlled).
