Personally, I have never had a problem with purchasing a phone from the website. Choose the phone you want, add it to your cart, log into your MyVerizon account, choose any changes(if wanted) to your account, provide the proper payment information and the phone shows up at my house.
If you would be more specific with what problems you are having, maybe someone would be able to help,
You could also call in or stop by a store to make the purchase.
definitions...
Verizon considers an "upgrade" simply to be purchasing a new phone at a discount when signing a new 2 year contract. It doesn't have to be a "better" phone, it simply has to be a "discounted purchase".
If you use one definition of a term and the entity making the sale uses a different termination, of course there will be disagreement. You have to use the definition Verizon uses to make any sense.
Not everyone wants a "better" or "more advanced" phone. Sometimes the phone they have has more capabilities than they want or need yet they STILL want to purchase a new phone at a discount. Verizon does not want to alter their marketing for EACH different reason someone may have for purchasing a new phone and therefore uses the SAME term for ALL discounted purchases when signing a new 2 year contract.