Argeon (Lyonar) and Kara (Vanar) are by far the most cost-efficient decks to build, ignoring the chance of you pulling exactly the right Epic or Legendary card. Lyonar only really needs Ironcliffe Guardian and Divine Bond, as can be seen here, with 3 Dioltas and 2-3 Holy Immolation being the only major upgrades for competitive play as seen here - Arclyte Regalia is really powerful but can be replaced with more bodies to control the board and receive Holy Immolation.
Kara is probably the best budget general of them all - looking at this S-Rank Kara deck from ManaGlow, you can see that the only cards that aren’t either Basic or Common are the 5 Legendaries (L’Kian and Spelljammer) being used to ensure that your hand remains full of minions to buff with your BBS. Substitute in cheaper ways of drawing cards (such as Sojourner and Blaze Hound) and you basically have the most powerful budget deck in the game - L’Kian is reasonably easy to unlock as you accumulate more Neutral Rares for other decks, so the only card that you’re actually paying full retail price for is Spelljammer.
Magmar is pretty strong as well. It’s historically been known as an expensive faction because of the prevalence of Magmar Control, which aims to drag out the game and capitalize on the late-game value of Legendaries such as Silithar Eldar, Pandora, Dark Nemesis and occasionally Khymera. On the other hand, aggressive versions of Magmar are far more affordable and Earth Sister Taygete gives you a huge power boost for completing all of the Magmar Rares - the deck really needs a full set of Makantor Warbeast to really shine, but the faction has gone from being a poor choice for budget players to probably being well above average once you’ve crossed the enormous tipping point that is unlocking Taygete. It’s pretty much impossible to say how much Magmar will benefit from the expansion without knowing how much stronger the other factions all become, since power level is entirely contextual on what your opponents are going to be playing, but there’s nothing that suggests that they’re going to do poorly.