Hi Cindy
If you're buying it, the main question is "what's affordable where YOU live?" But I would look for words "manure" or "compost:" on the bag. If it were me, I would buy one bag each of the cheapest few, take them home, and figure out which looked junky and cheap, and which looked richly organic.
I think even lawns need organic matter added to soil. Manure and compost provide that. Also, leave your grass clipping s on the lawn, or rake them around and in after they've dried up. Removing the clippings is like harvesting the organic matter from your soil and throwing it away.
I think any product made from chicken poo would be high in nitrogen, which lawns need. So I would look to provide something high in N, since your lawn seemed to appreciate the addition.
Figure the true price of the N by multiplying the weight of the bag by the first number of the "N-P-K" numbers , reduced to a fraction.
Say you pay $20 for 20 pounds of 10-10-10 "lawn food". That's $1 per pound of "stuff.
But change "10" to "0.1" (divide by 100 to change % to a fraction) and multiply 20 pounds by 0.1.
You paid $20 for just 2 pounds of "N". $10 per pound of N.
Say you pay $30 for 20 pounds of 23-16-19.
20 pounds x 0.23 = 4.6 pounds of N
That's $30 for 4.6 pounds of N, or $6.5 per pound of N. A much better value!
Just don't add too much! Concentrated fertilizer can "burn" roots and leaves, especially anything high in N.
Any kind of compost would be great. It could be made from any kind of manure, grass clippings, coffee grounds or other organic waste. But it won;t have concentrated N.
Organic sources of N will have the "N-P-K" numbers on the bag if you look close enough. They may be down around 1 or 2 or even lower. A 50-pound bag of Dr. Earth Whatever might have an "N" number of 2, for "2% N". Even if it only cost $20, 50 pounds x 0.02 = 0.1 pound of N. That cost $200 per pound of N.
Fresh, pure chicken poo with no straw or sawdust has an N number around 1.6% (multiply by 0.016).
That's wet, not dry. Dry poop is around 4%.
"Chemical" fertilizer usually has N numbers from 10% to 23%.
The advantage of manure or compost is that they have a lot of organic matter, and bagged "chemical" fertilizer has none.