When to go shopping:

Try to go shopping about five or ten minutes after the stores open in the morning. That way, there are fewer people around and you won't get (too) embarrassed. Also, the cash register lines would be almost non-existent. And finally, if you do get up the courage to go ask the women at the make-up counter in the more swank stores for advice, they'd be more likely to spend some time with you.

On-line auctions:

I have bought many pairs of shoes (too many!) on eBay. eBay's search feature makes it easy to find things that I want, for example, "red tank top".

Pay for an auction with a money order. Get a PO box so you can have stuff snail mailed to you. (See "Receiving stuff", below.)

You can also pay for most auctions with PayPal. Open an account via their Web site. Then deposit some money into your PayPal account by sending money (check, money order, etc.) in via snail mail.

Be aware that when you pay with PayPal, your real name (the name that you open the account with) will be in the email notifications that are sent to payees. So, if you don't want your real name known, don't use it. Or use only your last name. Or use first initial/last name, for example, "I. Last".

BUT.

If you do not use your real name, you may have trouble adding a credit card or bank account to your PayPal account.

Obviously, there is the potential for misleading or incomplete product description, or downright fraud, when buying from on-line auctions. I am happy to say that of the couple of dozens of things that I have bought via on-line auctions I have been bitten only once.

Receiving stuff:

Get a PO box and have your stuff sent to the PO box. You will need to give an address to open the PO box with, and I think you need to prove that you live at the address by showing a recent utility bill or credit card bill.