The Animal Crossing: New Leaf catalog is accessable from a machine within T&T Mart and later upgrades to that store, and includes:
That said, all items that are available in the catalog are not necessarily available for order. In some cases, this is true for entire classes of objects -- marked with a * above. Some rare furniture (such as furniture you earn as an achievement or receive through a special event) cannot be ordered. I will not list them all here, but some general guidelines:
- Nintendo items cannot be ordered
- Special Event items cannot be ordered
- "Achievement" items cannot be ordered
- Items dropped from balloons cannot be ordered
- Items obtained from the island cannot be ordered
- Certain DLC sets, like the 7-11 series, cannot be ordered. There are some exceptions to this. I'll keep a running list here and edit it as I find out more.
The following DLC sets can be ordered from the catalog:
- American Best Buy DLC. So far, the Raccoon Wall Clock is available for order from the catalog for 1,920 bells. We can probably assume that the remaining Best Buy DLC will also be orderable, but we will need to wait to confirm that as they are only released every 2 weeks.
- American Spotpass Content
- Japanese "Campus" Set
As to your second question -- yes, all you have to do to get an item in your catalog is to hold it. "Holding" is fairly popular in online AC trading right now. I've seen players trade fairly valuable items for the opportunity to "hold" entire furniture sets, or Japanese DLC items. Players do this so that they can fill out and complete their catalog.