A second vote for OSCommerce although a lot of small businesses use Actinic Catalogue. To use OSCommerce you need a web server capable of running php and MYSQl although I believe other databases are supported. As for integrating it you can either customise it yourself with a template or else call the PHP code from within your own web site. A good example of this is this very forum where the software in this instance is vBulletin but D-A-L has put the hard work into giving it a theme to fit in with the whole site.

As for payment processors, I use 2Checkout.com a lot and a similar product is available from www.paysystems.com . I believe NatWest are doing a similar UK-centric offering. If they've already got a merchant account then their bank will be able to provide a service ro else www.worldpay.com is a solid choice.