I think the waxy substance is a protective coating rather than a lubricant, so I always oil a new chain now, but I did find some problems with new chains previously.
As you say you have 'realised' that your old chain was worn out, it makes me wonder how you realised. In many cases, people realise that they need a new chain quite a long time after the chain should have been replaced. By that time, one or more of the rings, sprockets and/or jockey wheels may have been damaged by the chain. So there are still problems with a new chain.
If on the other hand, you realised when you measured the chain, which you do regularly, and it was looking more like an eighth stretched than a sixteenth, then it's much less likely that you've damaged the rings, sprockets and/or jockey wheels.
Cassette, chain, chainrings and jockey wheels are all new and I replaced them at the same time.
I haven't checked for a stiff link or the joining link. Tomorrow I'll clean and lube the chain... also check it for stiff links including the joining link.
M95* Mid/Short cage rear mech
M95* Rear shifter 8 or 9 speed
90mm Ringle Zooka