Ask the Agronomist(TM) says....
Lots of good info here. Her is my 2 cents:
Fertilizer- the organics are in many ways superior to the chemical fertilizers. By nature, they are slow release, but above all, since the good ones contain some form of manure compost, they provide micronutrients lacking in most chemical fertilizers. I am convinced that half the time the lack of a dark green color in many Texas lawns is not a lack of N-P-K, but micros like Zn, Fe, Mn, etc..... I use 90% organics on my lawn in the form of compost and products such as "Texas-T", but I will put on a tiny rate of straight N on occasion.
Weed control- here is where I part ways with many in the organic crowd. Corn gluten meal does work as a PRE-EMERGE, but I have never seen the 4-6 week residual others have. Most Ag universities would agree. It just breaks down too quickly in our climate. Vinegar and orange oil will SMOKE annual weeds (brown in a couple of hours in hot weather), but it will not kill perennials like dollar weed, dallisgrass, etc....without repeated treatments. It is also non selective - it smokes what it touches.
Fungicides- whole ground cornmeal works very well if you start at the first sign of trouble
Insecticides - lots of stuff here, and lots of it works
My bottom line to someone starting out is to go with the organic fertilizer, and if you have lots of weeds, go inorganic until they are under control. After that, a good organic fertility program and thick, healthy grass will keep them in check.