If you do not know anything about how to improve room acoustics, it can be overwhelming at first to understand all of your options. First of all, you should know what frequency of sound you want to absorb. For most settings, you'll just need to absorb the mid to high frequencies. An example would be an office or a daycare center, where most of the sound bouncing around the room is going to come from the human voice. In this case you'll just need to get acoustic panels. However, if you need to absorb low frequencies (bass), you'll also need to add bass traps. Examples include home theaters and recording studios.
The size of the panel is not that important. You'll just need to get enough acoustic panels to cover enough square footage of the room. The density of the material does not have much of an impact on the acoustic performance. A 6 lb per cubic foot density core material is not necessarily going to be better than a 3 lb density. The density just reflects to the rigidity of the material. If the material is rigid enough, you could just wrap fabric around the acoustic insulation and you would not need a frame to support the material.
It's also important to consider the fire rating of the acoustical panel. It's generally not a good idea to have flammable material hanging all over your walls. Many manufacturers may offer to topally treat the fabric covering with chemicals so that the fabric is flame resistant. This means the flames will self-extinguish if it catches on fire. Topically treated fabric will lose its flame resistance over time. Since the acoustic panels are not going to be washed, the flame resistance of the fabric should hold up over time, but it is probably a better idea to go with inherently flame retardant fabric if the fire rating is important. If the acoustic panels are going to be installed in places of assembly such as a church or restaurant, you will want to check with your local fire marshal or building inspector to make sure the panels will comply with your local building codes.
There are lots of companies that manufacture acoustic panels and sell them online, so you do have lots of options when shopping for acoustic panels. You can even look in your local yellow pages to find an acoustics engineer to help you treat the acoustics of your space, although this can be an expensive option.