I've used a lot of these cards almost since they were introduced to the market over a decade ago, so I'm drawing on my experience here (technical corrections are welcome):
Prepaid debit cards in the US come in two major classes: reloadable and non-reloadable.
Non-reloadable cards are purchased with a fixed amount of U.S. dollars on the card, and cannot be topped up. Once they are empty, they can be discarded. These are often sold as "gift cards", do not require an ID check, and can be found in most grocery stores, drugstores, shopping malls, etc. They generally have a flat fee for purchase of the card, and usually no other fees. The highest denomination I have ever seen for these is $1000, though I believe the law allows for them to have up to $3000. Most are in the $25-$100 range, though higher denominations can be found with some shopping.
You will receive a card immediately at the point of purchase, usually with the name of GIFT CARD or something similar. This once caused one cashier to glance at the receipt as I was finishing my purchase and tell me "Thanks for coming in today, Mr. Gift."
Reloadable cards are purchased with an arbitrary amount of money loaded on the card, and can be topped up at any time. These typically carry monthly fees, top-up fees, and sometimes transaction fees. They also require an ID check, and the issuer may restrict issuance to US residents. (Thanks, PATRIOT act!) They can be loaded with up to $3000 at any given time, though the issuing bank may have a lower limit.
Reloadable cards may have to be mailed to you at a US address; you do not typically get the card at point of purchase, though you may get a temporary card. The card you receive in the mail will have your name on it, and it generally takes about a week or two to arrive.
As far as I know, neither type can be obtained from outside the US; you must obtain them in person at a point of purchase.
Both types of cards will have a web site where you can register the card and associate a physical address in the US with it for the purpose of online shopping. The web site will also show the activity on the card and its current balance. For reloadable cards, the registration is mandatory and you will do it as part of the process of purchasing the cards. For non-reloadable gift cards, it is optional, and only needed if you wish to use the card to make online purchases.
(And those virtual cards you mention are only usable online; they cannot be used in physical stores.)
Which type is better for you, I think only you can say. But I would think that a high-value non-reloadable card or two would be the way you would want to go here. My favorite place to get them is at shopping malls; the mall customer service desk will sell them, generally in denominations up to $250 or $500 depending on the mall, usually for a fee of about $5.
Finally, a usage note: When your card gets near empty, you can instruct a merchant to charge the exact amount remaining on the card, and then pay the remaining balance via another payment method, as long as you aren't doing this at a restaurant, hotel or possibly gas station (since these places may authorize an amount higher than the amount given and settle the exact amount a few days later). This allows you to empty out the card and not lose any money.
You might also consider just using your own credit cards while in the US; if they have a magnetic stripe and are Visa, MasterCard, American Express, etc., they should work in most places in the US except for "pay at the pump" gas station pumps (pay inside the store instead). You'll usually get a good exchange rate, too, though this does seem to vary a lot by country and bank. Note that Maestro cards do not generally work for purchases here, though they work at most ATMs.