How should I introduce my wife? It just seems that 太太、老婆、妻子 are all either overly formal or make my wife sound older than she is (she's not even 30). Maybe one of those terms is actually more acceptable than I think it is; I don't know. Are there any other options that would be more socially appropriate?
When you introduce your wife both 太太 and 老婆 are acceptable, depending on whether it's a formal occasion. 太太 is more formal while 老婆 is more casual. Both are socially appropriate.

From 汉语词典：

太太：


（名）旧社会中通称官吏的妻子。 
（名）旧时官僚地主人家的仆人等称女主人。 
（名）对已婚妇女的尊称（带丈夫的姓）。 
（名）旧时称某人的妻子或丈夫对人称自己的妻子。


Although dictionary says it's used in past (旧时) , people are actually using this word more and more often in recent decades. If you are going to introduce your wife to new friends, business partners, or acquaintances, 太太 is the word you should use.

In comparison, other pronouns to introduce one's wife include:


老婆: used in casual and informal occasion, like with close friends or relatives. Especially, you can use this word to directly address your wife.
妻子: extremely formal. most likely only used in written language, e.g marriage certificate, court decision, etc.
夫人: rarely used to introduce one's own wife. Generally, 夫人 is used to introduce someone else's wife, to show respect (to the husband), cause the word 夫人 hints that the husband is socially recognized and esteemed.
内人: archaic. 
爱人: used to be the right word to introduce one's wife. But it was like 30 years back... Now it's also old and rarely used (only by senior people)
媳妇: acceptable in casual occasion, but only used in northern China.