"Game Economics" is a field all in itself and is part of the character of your game. Remember there is no right or wrong way, it is part of the game and if done well becomes the carrot that leads the player through the game. The economics, help them believe if they play just one more round they will be able to get that bigger gun.
You can do the health and gun strength linearly, add 20 to health each time, but increase number of enemies exponentially (using a polynomial as above). The choice is yours, provided it balances.
Ramp up difficulty to quickly and the player is overwhelmed. To slowly it becomes to easy. If they have to do some gold mining to get through the next level, it becomes a bit boring. To complicated and people will ignore parts of it.
A game with great graphics and sound, but bad economics is often still a bad game.
After the initial planning there is no substitute for play testing. Have fun.