Have you looked at the tools provided by 1&1 at all ?
Since you've chosen them as your host, why not call and ask them about their Turnkey eShops and other commerce solutions ?
They have a couple of alternatives to choose from and they could be termed more or less ideal for a newcomer to online trading since it's mostly wizard driven, although they may not be your cheapest option.
PayPal click here and their counterparts all have pretty good instructions on their sites. PayPal is arguably one o0f the quickest and easiest to set up, and possibly among the least expensive. Click the link on their site to Merchant Tools where you can read about how it all works and how to implement things. There's also a link to the PayPal shopping cart and similar features.
Is your account with 1&1 Windows or Linux hosted ?
This could be important in making certain decisions on how best to run things.
Post back with more detail and one of us will try and help further.