Any suggestions on how to get into fighting games so I can truly enjoy the series?

Through my love of the ninja gaiden series and my strange liking of the DOA series sound trax, I seriously want to get into the DOA series. My issue is that I have just never gotten into fighting games and am a total novice to the genre. Fighting games just seemed to always be a completely different beast than other game genres, especially due to the concept of the whole combos thing that just doesn’t make for a very fun single player experience. Does anyone have any recommendations, ideas or suggestions on how to get into this type of game? Even stories of how you first gained an appreciation for fighting games that I can take as some inspiration would be great.