Do not try to get forints before your trip. Just use an ATM in Budapest, being sure not to have the withdrawal recorded in dollars. I did not find a bank-owned ATM at the Budapest airport last month, so I mentally crossed my fingers and used the only one I did see, which was the not-usually-recommended Euronet. I'm still traveling and don't know how that transaction was recorded when it hit my credit union account, but there was no indication of a problem at the ATM itself. I was taking a cheap public bus (100E) into the city and walking from Deak Ferenc ter to my hotel, so I withdrew a very small amount of money (about $20 worth) just in case there turned out to be some funny business with the exchange rate at that ATM, but I believe all was OK.
Your back-up plan can be having a modest amount of nice, crisp US currency available in case you need to use the staffed exchange booth at the airport. That will most definitely cost you extra, but it's unlikely that you'll need to employ that back-up plan.
Tip: When you get to a bank-owned ATM and are ready to make a larger withdrawal, be aware that many Hungarian ATMs dispense the largest bills possible to meet your withdrawal amount. If you request Ft 20,000 (which is about US $80), the ATM may well give you one 20,000-forint note. Good luck trying to spend that. Obviously, you need to be aware of any ATM fees your bank is going to charge you, but otherwise, it's better to stick to small withdrawals so you get more-usable currency.
As always, switch the language to English on the ATM, watch for notifications of fees to be charged by the ATM itself (just cancel the transaction, retrieve your card and find a different bank's ATM), and do not let the machine record the transaction in dollars.
You should be able to use your credit card (assuming it's Mastercard or Visa) for nearly all non-trivial purchases in Budapest, but just as at the ATM, be sure the transaction is denominated in forints rather than dollars. Pay attention to what is happening with the card-reader. I had a problem elsewhere in Hungary with restaurant personnel taking it upon themselves to switch the currency to dollars, and that is a very bad thing, because they get to choose what (definitely not good) exchange rate you get.
As for how much money you'll need, I'm not a great judge of that. Individual tickets for local public transportation are Ft 350 (close to $1.50) if bought from vending machines (I used cash and don't know whether they take credit cards); I think it's Ft 400 or 450 if you pay the bus driver directly, and that would require cash. If you decide a Budapest Card is worthwhile, that will cover your city transportation (not the airport express bus I used), and you can buy the BC via credit card. My usual practice is to pay for small puchases, including low-cost museums, in cash, so I don't know what would happen if you wanted to pay a Ft 1000 admission fee with a card. The major museums seemed to take cards.
You do not want to over-withdraw forints, because they are not usable outside Hungary and converting leftovers to dollars at an exchange booth would be very costly. (Worst case, don't wait till you get back to the airport for that conversion.) I wouldn't try to guess the total you're likely to spend in forints; I'd just withdraw a modest amount and plan to hit another ATM if I needed to.
My beverage of choice is bottled water, and I had nice meals in solid, not-fancy restaurants for mostly not more than Ft 5500. Only once did I pay more, and it was still less than Ft 7000. Again, that's without alcohol or coffee, and usually without dessert. Note that many people would find it difficult to sit down to two full Hungarian restaurant meals in one day. But do watch out for sneaky servers trying to charge you in dollars. And take a look at the menu and (especially) the check to see whether a service charge has already been included.