So I was reading through and I can't really figure out if I've got this right. For a deck I'm making my monsters have 'During the End Phase: tribute this card then Special Summon 1 archtype monster from your deck,
Is this correct OCG and if I do not have targets remaining in the deck, do I still have to tribute for a cost-type scenario?
Yes, you would still have to Tribute. The way conjunctions work is that you still have to do the first part, even if you can't do the second part (except for "and" conjunctions), so you would still Tribute. Just to make your wording more correct, try this:
During the End Phase: Tribute this card, then Special Summon 1 "Archetype" monster from your Deck.