I recently created a shapefile in ArcGIS of my oceanic transform fault data. I started off with two separate files: a shapefile of points that simply contained a latitude/longitude and name for each fault; and a polyline shape file that contained the length measurements and the start/end points. I combined these two shapefiles in ArcMap using the "Join Data" command, and selecting to join the data based on spatial location. The result was a single polyline shapefile, that included all the original polyline attributes as well as all the related attributes (name, center lat/long) from the point file.
The problem was that the shapefile was not ordered the way I wanted it. In ArcMap you can reorder rows by ascending/descending values by double-clicking on the column header, or move columns simply by clicking on the header and dragging it over. The problem is that this only applies to your view of the shapefile attribute table, and the reordering is not actually saved to the shapefile itself. If you close out ArcMap, open a new map, reimport the shapefile, everything is back to the original order.
There is a free plugin tool for ArcGIS that is quite powerful and can solve these issues for you: ET GeoWizards. There are both free and paid versions of this toolbox, but I found the free version did exactly what I need. This toolbox is pretty impressive, and includes tools for feature translation, where shapefile objects are moved by a user-specified distance, filling holes in polygons, generalizing features, creating clusters from points, and a whole suite of other functions.
In order to reorder the columns and sort the rows in your shapefile, you can find the necessary commands under "Basic." The "Order Fields" command lets you select which fields you want to use from your original shapefile and specify the order in which they should appear. The "Sort Shapes" command lets you select which columns you want to sort the data by (you can select more than one), and whether you want them in ascending or descending order.
Another great toolbox plugin for ArcMap is Jenness Enterprises' Tools for Graphics and Shapes. If you are looking for a tool to calculate spheroidal (geodesic) length of features in your shapefile, this is the tool for you. While this toolbox includes many of the same functions as the GeoWizards plugin, it also has many unique tools as well. I have found that having both toolboxes has made working in ArcMap a much more pleasant experience. I wrote up a blogpost on the Tools for Graphics and Shapes plug-in back in 2010.