Sound is very important, especially if you use your backyard a lot. Remember when you buy a system; you are going to live with that sound for a long time.
Sound rating is measured in bels. Bels, similar to decibels, range from 0-13. The quietest units will have a bel rating around 6.8 with the noisier units rating over 8. Note: with such a small range for the bel rating on equipment, there is a significant difference between numbers. 9 bels will sound ten times louder than 8 bels. So a unit with a rating of 9 bels is going to sound as loud as ten 8 bel units. You get the idea.
We would not recommend buying any air conditioning unit with a bel rating of over 7.8. Your dealer can tell you what bel rating his proposed unit will have, and some dealers can even generate on their computer the actual sound of different air conditioning units. Unfortunately, this information is only available for the outdoor units.
For the indoor units, most of the sound generated is by air noise from the installation. There are many ways that a dealer can quiet this down, but they all add cost to the installation. This is another reason you don't want to go with the lowest bid.
If you have an installation now that is noisy, and the dealer only replaces the furnace and air conditioning unit, the indoor noise will probably be close to the same. If you the want the indoor sound reduced, you need to let the dealer know this up front so he can address it in his bid.
One thing you can do is put in a variable speed or two speed furnace. Since most of the indoor sound is produced by air noise when the furnace is running at low speed, this noise is greatly reduced. This only helps in heating though, as all furnaces must run at a high speed in cooling.