I suggest trapping as soon as possible. In the case of the kittens, the younger they start getting human interaction, the easier it will be to get them adopted—meaning the sooner they can be adopted.
Adoptability drops with age. 8-week old kittens get adopted before the 12-week old kittens. 9 month old kittens are old cats as far as adoption goes. The kittens will likely need fostering before they can go up for adoption. Count on 2-4 weeks for that.
Plus, by 16-24 weeks, the kittens can start making more kittens.
It's rare that kittens have to be TNRed. I can only think of one kitten that was so nasty that we were going to TRN him. In that case I caved in and "fostered" him for two years and adopted him last week.
In the case of the adults, they may or may not need to be TNRed. That depends upon how wild they are and the resources available. We have cats that have come from colonies that are immediately ready to go into homes (after medical). Frequently, such cats are just afraid of people and can be made adoptable by getting them used to us. Then we have others that take a lot more time and patience but are adoptable.
(As my previous anecdote suggests, my house is filled with TNR candidates.)
As how to go about trapping, you need to find a rescue group that will work with stray cats. In some places municipal "animal control" means just that. Our shelter is a rare one that does animal control but does not euthanize viable (as in physically survivable) animals (e.g., excludes blindness, FIV, FELV, diabetes).
You should be able to find obtain the placement rate of a shelter. It should be over 90–95% for cats. If 1-in 10 to 20 cats not surviving sounds high, you have to considers that most litters of kittens have at least one that does not make it. (Dog placement rates tend to be higher than cat because of the lack of a TNR alternative.) Many shelters have placement rates below 50%.
