Modern burn deck on a budget with combo synergy twist.
The deck centers around Underworld Breach, Grapeshot, and Electrostatic Field. All three benefit from having cheap burn cards, and all three synergize off each other.
Breach is cheap and gives fuel to Grapeshot both directly and via flashback. Breach fuels Field burn damage the same way. Field benefits from spamming spells for Grapeshot. Get all three together and its realistically an OTK.
The rest of the deck supports this synergy.
Consider/Thought Scour- puts 1/ 2 and 3 cards in the grave at instant speed and replaces itself. Absolute gold for all three combo pieces and supports the deck on its own in the early game when you can dump them turn 1-3 at instant speed and have a grave ready to go when you need it. Eight of them maindecked basically guarantees that you'll hit one, and potentially in opening hand where it's perfect.
Manamorphose- best topdeck you can get, as it trips all 3 synergy pieces, costs you nothing, replaces itself, and fixes mana problems (not that there really should be any).
Movement lands (Wilds, Islet, cycle lands)- 8 lands that aren't dead draws and full a grave and 4 lands that fill a grave and thin the deck. If you need mana, you get mana. If you need cards, they fill a grave and get you a card cheaply.
The rest is burn that speaks for itself.
Here's an illustration of an ideal game.
Turn 1- drop land, play blue cantrip (2 cards in grave)
Turn 2- drop land, electrostatic field (2 cards in grave)
Turn 3- drop land, play 2 spells for damage or movement (4 cards in grave, 2 damage from field)
Turn 4- drop land, pass or burn
Turn 5- drop land, pass or burn
Turn 6- drop land, bolt (4 damage), manamorphose (1 damage), breach, bolt from grave (4 damage), grapeshot (6 damage)
Which is 17 confirmed damage, so 11 cards in the deck played on turns 3, 4, or 5 finish the game.
Obviously that's an ideal game, but the idea here is that with so much synergy, at least one of the synergy pieces will surface and they all benefit each other and draw from the rest of the deck.
The build also has very few dead draws and takes advantage of deck thinning to synergize with everything.
Plus Field has a fat ass and can take a bolt or a block and either survive or go 2 for 1, and he's cheap so you come out alright even if he gets canned.
I particularly love Needle Drop in this build, as there should be no problem getting it to cast as the whole deck causes burn damage, and its deliciously cheap and replaces itself. Needle Drop plus Field is 2 damage and a card at speed that fills the grave and is a perfect flashback, all of which helps Grapeshot.
I'm years out of the meta and don't think this deck will stand up to true competitive play, but it's an idea on a budget and I think it at least has potential.