I personally prefer Zencart.

I'm going to cast another vote for ZenCart. I have found it easier to work with in the past.

Yes they can be integrated into a site. The appearance of the cart can be customized, with stylesheets, to look similar to the colors etc. of the main site. Some people have the home page of the cart as the site main page, and others link to the cart's main page.

I haven't tried oscommerce but have heard that it is harder to customize than zencart.

I did do one zencart installation and customization. The Zencart forums have a lot of information. Be sure to search before posting questions, as they were a little abrupt with people who asked something that had been dealt with a million times before.

There are plugins that extend zencart's functions (such as shipping from Canada, which I had to deal with for my customer). I am sure that Oscommerce provides them also.

If you do use zencart, be sure to read how to set it up so your customizations of the skin are protected from being overwritten with any updates. It's using the english/custom folder setup, and I'm sorry I don't have that bookmark but look for the directions to do this (it WAS in a long post) in the setting up zencart documentation at the forums.

The file structure of zencart is also a little confusing when you're new, I mean for the developer, not the customer. Some sections, such as the text on the home page of the cart, are in more than one place. Take notes of changes you make and to which files and where they are in the folder organization. I had to fix something for my customer a couple of months ago, and this was 18 months after doing the cart and I had to go back and dig to find what I'd done before. Live and learn!