Resurrect Priest is a Tier 3 deck right now, succeeding because of its ability to summon tons of huge taunts and leverage their high health totals for Divine Spirit + Inner Fire kill potential. This budget list comes in at under 1500 dust by sacrificing a few legendary cards, but is otherwise very similar to the default list and retains the same functional win condition. And don't freak out, Northshire Cleric is standard despite the resurrect pool implications, card draw is still important! This deck will be quite competitive up until at least Rank 5, then may struggle depending on the meta you're seeing.
You can also watch me play this budget deck and more on Twitch below: