Just because the bank says you can, doesn't mean you actually really can afford that much. The bank doesn't take into account any of your other spending habits, besides the fact that that's the limit, not the goal. Ultimately it's your money, your house, your call, but you don't want to end up house poor just because the bank said you could. Also consider like you said that interest rates will rise (they are as we speak) and you will be able to afford less if housing prices stay the same

As to the 20% down, you'll get a lot of different opinions. PMI honestly isn't that bad - ours was going to be only fifty dollars extra a payment. Yes it's throwing money away, but it wouldn't necessarily make or break anything. The thing that we focused on, however, was getting the monthly payment down as much as we could, and that meant putting 20% down. It's kind of just what's important to you.