So both those are reasonable if you read the meta right. I would also say that depending on what budget means (0-proxy vs 5-10 proxy vs infinite proxy) and also how much money is budget for you ($400 vs $1000 vs anything but power/shops/bazaars) makes a big difference in answers to this question.
In general I would tend toward unpowered blue deck over something like red prison in vintage? In a 5-proxy meta I would do this every time (3 mox/lotus 1 time walk 1 ancestral, and the rest of the deck is legacy cards).
Budget decks are all going to be somewhat limited in power level. You can, however, key in on a big matchup (or two) and get a service-able deck that can go on a run when it hits its matchups. With all the recent printings, I’d look long and hard at GW hatebears. You can cover a lot of ground with access to 12 Null Rods, and various GY/storm hate options.
@Brass-Man also had a really cool BG survival deck that could very easily be made powerless. It also had very few (if any) duals.
Moxen in that deck aren't really great, -you play Collector Ouphe which shuts them off. They also can't be tutored with survival and Elvish Spirit Guide can be.