Are there any good budget decks for Eternal?

There are some very good budget decks that players have put together, to help you get into the game fast. 

Hyper aggressive - https://eternalwarcry.com/decks/d/-kJlbqMPm2M/true-budget-deck-for-new-players-no-rares-no-adventure-cards

Less aggressive, but still aggro - https://eternalwarcry.com/decks/d/vg8e-9xnGr8/budget-argenport-gunslinger-scums

Yet another aggressive deck (most cheap decks are aggressive): https://eternalwarcry.com/decks/d/NYuJCK2lNo8/a-budget-rakano-aggro

A budget midrange deck: https://eternalwarcry.com/decks/d/66GHn5IcezQ/budget-fps-mid

You can also search the deck website yourself for budget or starter decks, www.eternalwarcry.com

There was a recent nerf of popular Justice (green color) cards that easily kill your minions, so budget decks might get better except for Yetis, that is no longer good anymore.

Indeed, that should help with meta diversity a bit; though, to be honest, the meta is pretty diverse right now. It's mostly in a pretty good spot.

For Expedition mode, one of the top 10 players in that mode (who is famous for creating good budget decks) just wrote up his guide for Expedition Budget Decks. Here's the link to the reddit post of it.