Glad to join this forum. I am from 'Hometown of goji' and feel upset with much false information regarding goji on the internet. I am developing a website attempting to share what I know about goji and hopefully you may find interesting.*Below is an excerpt from my*goji knowledge base. I also attach a photo of the best Lycium barbarum cultivar developed so far.
Let's talk a little about goji variety and cultivar before reaching 'propagation' topic. Currently in the US goji market is full of false information and groundless claims. I address the importance of cultivar because growing good cultivar would avoid wasting your time and money on a inferior variety that may end up with very dispointing result. I have heard many complaints of bitterness taste of some kind of goji, one very possible cause I can think of is wrong varieties are selected. For example pale wolfberry, a native variety to North America, has bitterness taste. Its scientific name is Lycium pallidum Miers, instead of Lycium barbarum (goji variety of documented medicinal value). Saying this I am not denying any potential medicinal use of pale wolfberry, but for goji in common sense, pale wolfberry is not we are talking about. Sadly seeds of Lycium family (which include many varieties)are sold on market and goji growers blindly accept what are available on market
In summary, goji variety and cultivar matters if you are serious in growing goji. The best goji variety with documented medcinal value is Lycium barbarum (its common name is Ningxia goji, Zhongning goji, Shan goji, Xi goji, etc.). The best goji cultivar of Lycium barbarum is 'No 1* of Ning-qi'.
Besides cultivar, environmental factors also play important roles in quality and yield of goji I will discuss this topic later. There are two ways of propagating goji plant: by cuttings or by seeds. When a good cultivar is selected, it is always better to propagate this cultivar using its cuttings, so that the seedlings grow from the cuttings preserve all super characteristics (traits) of their parent cultivar. You can also grow goji from seeds, but keep in mind the plants grow from seeds may not be the same as their parents. After long history of natural and artificial selection, there is no 'pure' bred. Everytime you propagate goji from seeds, you obtain plants that are different from each other due to 'gene segregation'. Some of the plants may be like their parents but others may be different in traits such as leave shape, berry shape, branch stiffness, etc. So you can imagine after many generations of self-crossing goji cultivars would lose many good traits like high yield and disease tolerance that were formed during controlled selection over the history.
So the conclusion is
1) growing goji from cuttings of a good cultivar (like 'No 1 of Ning-qi' if available.
*2) if cuttings are not available, you can start from seeds of the best cultivar*you know. In that case, you may have some plants the same as parent cultivar and other plants different - they may be the same as their grandparents (cultivars that were used to develop the best cultivar). Propagating goji from seeds is a compromise, but if you start with seeds of best cultivar, you are still in good position - you are not on top of the pyramid, but only miss one step
3) Do not use seeds from plants that grow from seeds! The reason has been stated above.