The biggest - and hardest-to-follow - rule in homebuying is that friendly real-estate agents and mortgage brokers don't actually work for you, no matter how much they act like they do. They work for themselves, and they earn money based on the prices (and interest rates, for brokers) at which the deals close.
This means the real-estate agent wants you to buy a house for the highest price she can talk you into accepting, and the mortgage guy will give you the highest interest rate he thinks you'll agree to.
But if you spend all your cash on the down payment, and lock up all your monthly income in a mortgage payment that's too high, you'll become "house-poor" — you'll have a house, but no money to improve it or fix anything that might break, and you'll risk being unable to make the payments if unforeseen expenses crop up.
So, buyer, beware - and be patient. Don't let other people pressure you into something you don't want, and when you find something you do want, bargain with them to get the best deal for yourself.
Your real-estate agent will ask what your price range is. And then she'll try to show you houses with asking prices "just a little more" than that. That's her upsell trick - if you fall in love with a house that costs more, your emotions might take over, and she'll make a bigger commission - for ignoring your initial request.
Once you've found the right house, your agent will start negotiating for you. She'll probably ask "How high are you willing to go?" But your answer is not just giving her information that can help her make a deal on your behalf; it's giving her tacit permission to set your highest price as the final amount (which makes her a better commission). Just tell her what your offer is at that moment.
If a counteroffer comes back, consider it - on your own. Multiple rounds of offers and counteroffers are quite normal - though your agent may push you to make big concessions to close the deal (so she gets paid sooner, and for less work).
Mortgage brokers will pull similar tricks, trying to get you to take a higher rate - which gets them better pay. If you want something lower, keep pushing, and keep waiting.
Above all, remember that right now, houses aren't moving. Agents and mortgage brokers are sitting idle, hoping to close deals to get some income for themselves. So drive a hard bargain - even with the people who are "on your side." If you make it clear that your offer is your offer, and you're not moving, your agent will work really hard to close the deal. If you are unambiguous about wanting a lower interest rate or better terms, your mortgage broker will step up to the plate for you. But you must make it plain that you know the market favors you, and you're willing to wait.