This is my take on a competitive Persist deck, built on somewhat of a budget. The only expensive cards in the deck are cards I either already own (Ignoble Hierarch, Profane Tutor, Yavimaya, Cradle of Growth) or are main combo pieces and/or are cards I feel are necessary for the consistency of the deck (Altar of Dementia, Melira, Sylvok Outcast, Nurturing Peatland).
The game plan is pretty simple. First, get out any of the persist creatures, Kitchen Finks, Putrid Goblin, or Safehold Elite. Next, cast either Grumgully, the Generous, Melira, Sylvok Outcast, or Thran Vigil, which removes the -1/-1 counters placed on the creatures from their persist trigger when they die and return to the battlefield, making them essentially immortal. Once that's set up, put out either Altar of Dementia, Goblin Bombardment, or Viscera Seer for infinite free saccing and win through either infinite mill, burn, or life gain triggers. Profane Tutor might not be completely necessary, or even that great since you have to wait two turns to actually use it once you pay for it, but having a couple of them helps boost consistency since there's so many different pieces to the engine needed to pull off the combo.
It's a fairly reliable turn 4 win, but with a budgeted and weaker mana base like this it sometimes takes to turn 5. However, with a god hand it can win on turn 3. The perfect hand for this deck looks something like this:
Opening Hand: Ignoble Hierarch, Putrid Goblin, Thran Vigil, Goblin Bombardment, Forest, Mountain, Swamp.
T1. Play the Forest then cast Hierarch.
T2. Play the Swamp then cast Thran Vigil.
T3. Play the Mountain then cast Bombardment and the Goblin, then sac the Goblin to Bombardment as many times as it takes to win.
Any help on the sideboard would be greatly appreciated as I’ve never actually made a proper competitive sideboard before. So, if you have any comments on how to improve the deck and/or sideboard (while keeping it reasonably budget) or have any questions about it, let me know! Thanks in advance!