Bear with me here--this is a long post and I am going to go out on a limb because my take on the interest rate vs. price is a little different than most. It seems EVERYONE says that interest rate is most important. Well it probably is in general and for the everyday homeowner's monthly payment, and if you are only talking about paying an extra $5k for a property and getting a super low interest rate I would typically agree. People often even pay $5k or more just to buy down their rate, or overpay by that much or more to get seller financing or better terms, etc.
But the flip side that I never hear ANYONE talk about, is that if you overpay for a property you have overpaid and there is no way to change that. There are multiple ways to manipulate the interest rate (refinance, sell, pay off, etc.), but you only get one shot at buying for the right price. Most people tend to sell or refinance every 7 years anyway. If you are planning to buy and hold for 50 years and never refinance, you may have a lot of capital locked away that is no longer helping you buy more property.
There is also a reason that hard money lenders exist--you can WAY overpay on the interest rate up front if you buy right, but you cannot ever get out from overpaying (except through foreclosure/short sale/etc., which I don't include).
I think you need to factor in both (among a variety of other things), but I certainly wouldn't overpay (by much anyway) to jump in now just because rates are low. And if/when rates go up, property values tend to stagnate or decline anyway...
It sounds like you are also only considering conventional financing. There are a lot of other avenues of buying/financing property (such as seller financing, private money, cash, options, sub-2, trading, partnering, etc.). The interest rate is only one factor to a deal, and frankly I think it is silly to overpay for a property just on the premise that interest rates are low. Yes the interest rate is an important factor, but it is not everything.
I remember sitting in the living room of the apartment I was renting in 2007 watching Suzie Orman babble something about buying a house, and I was going through the same thing then that you are now--thinking I have looked everywhere and tried everything and the numbers just didn't make sense, but to me they didn't so I didn't buy. I made offers and had a few things under contract, but pulled out of all of them for one reason or another. I was frustrated and didn't like the idea of continuing to 'throw my money away' on rent every month, but most of the people I know that did buy then regretted it. All that money I 'threw away' continuing to rent saved me 10 times what I paid in rent for a few years. I then came in and bought a house a few years later from someone that took the plunge and found out later the numbers didn't make sense...but they got caught up in the hype and the 'buying something to buy something before they were all gone', and they way overpaid. I would still say owning is better than renting, I am just saying it doesn't make sense to buy just to buy.
Look at the whole picture, establish YOUR criteria for what makes a deal worth buying, and then only buy if it fits your criteria.