As another answerer already mentioned of course, decibel level is of concern - you don't want your kids listening to music that is so loud, you will actually hurt their hearing.
Outside of that, as shared by this poster some studies on music and toddlers have shown that there can be some impact on intelligence, while still others seem to indicate that is a load of hooey, or that the impact is miniscule. Even the criteria that music not be too chaotic or discordant, is a tough one, because the assertion is often then made that classical is the way to go. However, there is plenty of classical music (or romantic or modern era "concert music" which are also often referred to as "classical") that is "chaotic and discordant" Beethoven's second or Fire Bird or Rite of Spring by Stravinsky for example.
As someone with a lot of training in child development and experience in both the two's and three's classroom in preschools, I decided not to worry about "researched" aspects of music choices for my own child too much. Instead of focusing on a specific type of music as "okay" or "not okay" I focus on the music itself. As teacher and parent, I pay attention to:
Is there language in the lyrics (particularly in the repetitious portions) that would be embarrassing to my child, myself, or teachers and other parents with whom she interacts regularly, or are there lyrics that are overly educational about inappropriate topics for her age group (explicit sexual references, topics on death, suicide, crime etc. - my allowances or lack thereof for these types of topics change as she grows and changes and is more ready for certain things). I try to think, if she repeated any of the lyrics in mixed company or to a little friend would I feel bad about having let her learn the song? (If so, I avoid it when still with lyrics). If you have some favorites of yours that contain such lyrics, you might try Lullaby renditions of. . . or see if the Vitamin String Quartet has covered what you like without the lyrics)
Does my kid or do my students respond to the music and what kind of a response is it? Music does impact mood - if I notice that a particular piece of music - or genre of music seems to create grumpiness, I nix the music. Of course if a piece of music you get out startles your child, it would also fall into this category. Conversely, if my child seems soothed by a certain piece of music I put it in the "soothing" playlist, OR, if a song is upbeat and makes her want to dance and laugh etc. (Or in the case of nine-month old, giggle and clap), I put it in the "play time" playlist. - You get the idea. One play through with a piece that has a negative impact is not going to do lasting damage. As they get older and more communicative, they can talk to you about their perceptions in this realm more and more too. In regard to this one, at nine months, I presented what I liked and fit with Criteria number 1.
As annoying and repetitive, as children's music (and some pop) can be, kids learn from repetition and some of it is really pretty good. I would include some honest to gosh "children's music" in your repertoire. Songs like, "Jim along Josie" and Animal Action songs are great for teaching different types of movement. There are songs that teach days of the week, numbers, etc. Even songs like, "I like to eat a apples and banaynays" can be really useful because of the teaching behind them (this one teaches the vowels). Songs that include fine and gross motor skills all help even with language development as well as rhythmic development and aquiring musical appreciation. At nine months, songs like, "teddy bear's picnic" and "Animal Crackers in my Soup." are fun and capture imagination.
Do I like the song At ALL If listening to the song over and over again is going to put me in a bad mood because I just can't even tune it out because it sounds so awful to me (for example, anything by Lady GaGa), it is not in my child's best interest to have it playing because I will eventually be in a bad mood over it - not conducive to constructive interactions with my child.
Outside of those considerations, As my child grew into toddler-hood and beyond, I have tried to give her variety. To me, filling the house with a variety of genres keeps things fresh and my daughter informed as to the musical options out there. At the preschool we were required to play a variety of genres and even had a rotating featured genre each month that was required we play. The director spoke as though she had learned about benefits of a variety through some of her training, though I cannot think of any specific study I have ever read or heard about in this regard. Doing searches for "Top Tens" and then a genre will often yield songs you can preview and choose amongst. Many times you can find one or two that fit the above four criteria (and if you don't find something you like, don't worry about it). This article provides a list of a variety of resources for finding great music that is also great for kids such as those given in the links in the first criteria I listed and might be of particular interest to you right now for finding songs from a variety of genres that might work for you. One of the best resources listed in the article for achieving variety is baby loves music.
I have written a few articles about music and kids on my blog that you might find interesting if your child really takes a liking to music and you want to give your child a musical education/enrichment experience. My blog is pinchxeverthing.blogspot.com.
While this question is designed to ask about what music is good for babies still in the womb. Many of the same concepts apply, so if you have not done so already, I'd check it out too.
In regard to the criteria you offer, I'd disagree unless you are thinking specifically for music in the "soothing" category. My daughter loves (and has long loved) "Ride of the Valkyrie" by Wagner. "In the Hall of the Mountain King" is another favorite even though it is fairly loud at the end. She also loves "1812 Overture" by Tchaikovsky (Loud Timpani, Cannons . . .). Sometimes big changes or dramatic shifts in musical dynamics can be really fun for kids as well as teach them vocabulary like loud and soft (or forte and piano in musical terms) by setting up the example for you to discuss. Have fun!
