Where can I get a Master Card or Visa Card for on-line Internet
purchases that will best guarantee against fraudulent mis-use? 
Ideally, a one-time-use number that would be limited to the actual
amount of the purchase and not be (fraudulently) re-usable?

Check with you existing credit card company.  Virtually all of them
offer their customers access to a one time use number.  I know for
certain that citibank does.

We use a ShopSafe service provided by MBNA Visa card. It allows to
create a card number with specific spending limit (i.e. the amount of
your purchase), which can be used only by specific merchant. Later, if
you want to do business with the same merchant again, you can just
increase spending limit and extend the expiration date.

The MBNA website knows nothing about one time/temporary use
creditcardnumbers and my bank (Bank of America) says it doesn't offer
such a service for its credit cards.  So, I remain at square one!

Here is the link
https://www.mbnanetaccess.com/NASApp/NetAccess/AboutShopSafeDisplay
We use ShopSafe with AAA Visa card (provided by MBNA). It may be
available with other cards from MBNA.
Hope this helps.

Alas, the MBNA "shopsafe" service is not described or offered anywhere
on their public website and the link
offered(https://www.mbnanetaccess.com/NASApp/NetAccess/AboutShopSafeDisplay
) is for exitsing customers with an account number.  

So, still at square one...

Check these link out:

http://www.citibank.com/us/cards/tour/cb/shp_van.htm

http://www.auctionbytes.com/cab/abu/y205/m02/abu0137/s02

http://news.com.com/2100-1017-245428.html?legacy=cnet

Here's the information re MBNA.  It's not on their public website,
only on their secure website:

Protect your real account number when you shop online. Use ShopSafe to
generate a temporary account number, and complete your online purchase
with confidence.

Here's how it works:
Shop online as usual. When it comes time to make your purchase, just
log into ShopSafe. Enter the limits you desire, and ShopSafe will
generate a temporary account number so you can complete your
purchase.....just like a regular card!

Optional download:
Get extra features when you download ShopSafe straight to your desktop:
-  Desktop icon for quick access
-  Help filling-in checkout forms
-  Direct link to Net Access for account information

Questions and Answers
Q: Is there a maximum number of credit card accounts I can use with
the ShopSafe service?
A: No. But all accounts must be credit card accounts registered in Net Access.

Q: Where can I use the ShopSafe account number?
A: The ShopSafe account number will be accepted anywhere your MBNA
credit card would be accepted. The online merchant does not need any
special software or applications to process your ShopSafe account.

Q: Can I use ShopSafe for recurring payments?
A: Yes. Some subscription services such as book clubs and Internet
service providers, require recurring monthly charges. The ShopSafe
service allows you to set your "Valid Thru" date for up to 12 months
in the future. The Recurring monthly payment located on the Credit
Number screen allows you to securely manage your monthly bills.

Q: Can the same ShopSafe account number be used to make purchases at
more than one merchant site?
A: No. To provide additional security at each merchant site, a new
ShopSafe account number needs to be generated for each online merchant
site. However, you may reuse the same ShopSafe account number at the
same merchant site.

Need more details? You'll find additional information about this and
other services in NetAccess help pages.