Being an avid knitter who just happens to be allergic to 'most any animal fibers, I have great experience with various brands of acrylic yarn. My all-time favorite is Red Heart Light & Lofty, a weight group 6 - super bulky. It knits up quickly, is deliciously soft, and goes through the washer and dryer (warm and medium) effortlessly. It lasts for years and even reblocks itself when machine washed and dried! Oddly enough, it can be hard to find. I recommend shopping online to get the best selection for this yarn. The same yarn comes in three different color classifications, each of which has its own label: Light & Lofty, Bright & Lofty, and Baby Clouds.
Coming in a close second is Michaels stores' Loops & Threads Country Loom. It's also a 6 super-bulky. I've only used it a couple of times, but it handle really well and says it's machine washable. I haven't tried yet.
Both of these are in the $3.- to $5.- range per skein. The skeins are about 100 yards long and weigh 4 to 6 ounces.