Relating properties and structures of polymers
I think that the best thing for you to start with is to compare the radical formed low density polyethylene (LDPE) and the Ziegler-Natta high density polyethylene (HDPE).

The low density polyethene has plenty of side groups which are randomly arranged through the length of the chain, this can be regarded as a copolymer of a range of different alkenes which are randomly arranged.

The high density polyethene (HDPE) is an almost perfect homopolymer of CH2 units, this polymer has far better mechanical properties, it is a polymer where the chains pack closer to each other than the chains in LDPE.

There is a version of HDPE which has properties closer to that of LDPE, this is formed by using a mixture of alkenes using the organometallic Ziegler-Natta cataylsts.