How do I buy bitcoins in USA?
For anyone else who's in the same situation...

I had some some fairly detailed discussions with some helpful folks on the #bitcoin-otc IRC channel and they gave me the scoop. To avoid getting hit with large transaction fees and/or revealing your name, SS#, routing numbers, etc., you really need to go over-the-counter. 

In some cases that might mean doing the deal in person (localbitcoins.com) but a safer way is to use MoneyPak. It was described to me as follows: You buy a moneypack in whatever denomination you're interested in converting to BTC, and you provide the MP number to the seller. He, in turn, sends the coins. He can use that moneypack number to load his PayPal account and buy goods/services. The fee is $4.95 -- not unreasonable. And everything is anonymous. 

The other point that was made crystal clear to me is that you can't just jump into the OTC community and start doing large volume transactions. The liquidity is there if you know where to look but the community has to trust you first. They even have a rating system.

I was walked through the initial steps of reserving a name, creating a GPG key, binding that to my identity, etc. etc. and will probably execute a few small-sized moneyPak-based transactions ($10, $50, etc.) and see how it goes. 

Hope these comments will be of value to other new Bitcoin enthusiasts.