Curve Theory
When to level to the next tavern tier and when to buy minions or utilize your hero power instead, is a whole lot of theory on its own and greatly depends on the hero you are playing and also on the cost to use its hero power.
The standard/basic curve is buying one minion on turn 1 (3 gold), going to level 2 on turn 2 (4 gold), selling your minion to buy two minions on turn 3 (5 gold), buying two minions on turn 4 (6 gold), buying one minion and going to level 3 on turn 5 (7 gold), rolling and buying the best two minions on turn 6 (8 gold), and going to level 4 on turn 7 (9 gold). After that, deciding to level to 5 or 6 will heavily depend on your board, which discover you get from your first triple, and even your opponents boards.
If you happen to get an early minion that can generate gold value for you (the most prominent example being Deck Swabbie) you can either gain some tempo by buying two minions without having to sell one on turn 3 (5 gold) or alter your curve aggressively to level earlier (for example going to level 3 on turn 3 (5 gold) without having to sell your minion).
If your hero power activation costs 1 gold and is worthwhile early on you can alternatively play the so-called Rafaam curve going to level 2 on turn 4 (6 gold), going to level 3 on turn 6 (8 gold) and going to level 4 on turn 7 (9 gold).
For further information about the different kind of curves and which hero prefers which, please refer to the Battlegrounds Curvesheet by Minder and Jkirek and the accompanying graphical curve guides.
Please note: In the currently active spell meta of season 7, following a curve plan per hero is not as important as before. The spells offered can often smoothen your turns in the early- and mid-game. Due to that the curve sheet is currently on hiatus, but the basic principles can still be applied to your games.