Here's an important principle that I don't see discussed very much in the literature but is common among top players.
Suppose you open 1♥ and the auction is 1♥ - (2♣) - 2♥ - (3♣). You have some extra values and want to invite game in hearts. The way to do this is to bid 3♦. In this way you also have the options of bidding 3♥ just to compete (typically with minimum values and a sixth heart), or doubling for penalty. Your 3♦ says nothing about diamonds, it just happens to be the only suit available for this.
Next, suppose it goes 1♥ - (2♦) - 2♥ - (3♦). Now there is no intermediate suit bid available for a game try. In this case we use the double as a game try, giving up on a penalty double, and 3♥ is still just competing. This is called a "Maximal Double" and is further described here:
https://www.bridgebum.com/maximal_double.php
Now consider 1♠ - (2♣) - 2♠ - (3♣). Here there are two intermediate suits that you can use as a game try, and I suggest picking the one that most closely matches your game tries without competition -- perhaps a suit where you have length or something of value.
This same principle applies when yours is the overcalling side. For example you overcall 1♥ in this auction: (1♣) - 1♥ - (2♣) - 2♥ - (3♣). 3♦ is the game try and other choices are natural as above.
The "Bridge Bum" site is a great resource for details of many common conventions. For more about game tries in general see:
https://www.bridgebum.com/help_suit_game_try.php