I would have said go for the new class' cards but everything else is building to beat that class & it's not so fun anymore.
Personally I would recommend the super fast Face Hunter. Not many expensive cards. You either win or lose within 5 minutes. https://hsreplay.net/archetypes/355/face-hunter
There are a few more cheap-ish competitive decks currently. A lot of clearance cards are single-target so building a wide board is working.
Spell Druid's only legendary card was free. It's currently one of the best decks. https://hsreplay.net/archetypes/372/spell-druid
Totem Shaman is a brand-new archetype that is supposed to be quite good. I haven't tried it yet. https://hsreplay.net/archetypes/201/totem-shaman
Murloc Paladin is still going but could probably be easily countered in the future. https://hsreplay.net/decks/WkZBvNR6vSZY9FuFh1gUmb/
Most other classes are quite expensive I think. Lots of essential legendaries & epics.