Welcome. It will be a fun expansion for you. If you stick around here long you will find there are really two sets of people. One that believe in bridge programs (using both organic and chemical compounds in their programs) and then the organic only. I am bridge. I catch crap for being so, especially when I challenge some of the extreme statements made by the organic only people. Which one you decide to be should depend on you, your preferences, and those of the people in your area (you can't sell a product or service that people don't want). Others may try to convince you how horrid your chemicals are and that you MUST go all or nothing. I personally don't believe it.
Anyways... this may help you connect with your current thinking...
Being synthetic you should be able to run the numbers and calculate application rates. Suppose you put down 1/4" of compost. This equates to roughly .8 cubic yards. A cubic yard weighs roughly 1,000 lbs by moist weight. Dry is about half that weight. Thus you are applying roughly 400 lbs dry compost per 1,000 square feet of grass. Knowing application calculations as the good steward you are should allow you to figure how much NPK you are really putting down.
400 lbs dry per K multiplied by...
1.7% N = 6.8 lbs N
.84% P = 3.36 lbs P
.77 Lbs K = 3.08 lbs K
6.8 lbs N is quite a bit. Now you must understand that this number probably reflects total N. In which case, most of it will not be plant available the first year. (roughly 5 to 10% of N from compost is made plant available the first year, depending on the compost and/or maturity)
Usually this is enough. Sometimes it isn't. When it isn't you must ask yourself how you are going to supply just enough nutrients from other sources (organic or not) to get the result without adding too much.
As far as weed control... the only effective organic system so far is cultural practices. Keep the grass healthy and long (usually no shorter than 3.5 inches) and most weeds can't take any ground.
Insect control is similar. There are various oils and nematodes (tiny worms) that you can apply if you want to stay organic, but I have found them to be too hit and miss for the standards of this area.
Fungal control is similar. Cultural practices first. Let the lawn & soil surface dry out between watering. However, there is a pretty effective natural product called chitin (or various enzymes related to it). Bill sells it as his 123 NPP. ICTorganics.com