Essentially there are 4 types of autocad data you can export.
lines
polygons
points
text
Text will export as a point.
There are many features that will export as multiple features. For example Blocks will export as points, lines, closed lines, hatch polygons etc.
Instead of exporting the AutoCAD dwg as shape files try opening the dwg directly into ArcGIS and do queries to select various layers in the drawing and export them to your database.
There really is no simple way for me to explain the entire process. A good share of my current career has been spent converting AutoCAD drawings to ArcGIS. There are a lot of tools built in for dealing with AutoCAD but I have found it is simple grunt work that gets it done the best.