If rates go up a LOT, then this will just drive the price down and the overall payment may therefore stay relatively level.
Personally, I think the best strategy is to save AS MUCH MONEY AS YOU CAN and buy when the rates are high. This is also hopefully at a time when nobody else is buying (due to rates, or whatever) and so you’ll find a nice place without some stupid bidding war.
Then, when rates come down, refinance!
You can’t do it the other way – once you’ve got the low rate, there’s nowhere to go…