Those three verbs have related, but different meanings:
"Liefern" can be translated as "to deliver". It encompasses the whole range, so to speak, from the sending to the receiving.
"Wegschicken" can be translated as "to send away". In the context of a delivery it would be quite casual. In a business context, I'd rather use "abschicken" ("to send off" or "to send on its way"). Both, "webschicken" and "abschicken", only refer to the sending and say nothing about the receiving.
"Ankommen" can be translated as "to arrive". This verb, on the other hand, refers to the receiving or the arrival of the goods and says nothing about the sending. More technically, you could distinguish between "ankommen" and "erhalten" ("to receive"). Because the goods could have arrived at your place, but you didn't receive them (because the postal service put the package behind the shed or something).
So, which verb you use depends on what exactly you want to complain about: Did the goods not get delivered? Did the merchant not send them off? Did you not receive them?
As a side note, you're missing an "e" with each three: It's "nicht gelieferte Artikel", "nicht weggeschickte / abgeschickte Artikel", "nicht angekommene Artikel".
EDIT: Another side note that I didn't notice when I wrote the original answer, "sich beschweren" is used reflexively:
Ich bin hier, um mich über ... zu beschweren.