Whether to keep you new kitten as an indoor only pet, or allow some (or a lot) of outdoor time is a personal decision. The indoor lifestyle is definitely a safer one for our cat friends IF their environment is enriched in such a way that allows and supports innate behaviours (for general indoor cat considerations visit: Basic Indoor Cat Needs). Kittens and cats lacking appropriate environmental enrichment are more likely to have behavioural problems such as anxiety related excess grooming and spraying/urinating outside the litterbox, as well as conflict among house-mates, and medical problems such as Idiopathic Cystitis that can result in life-threatening blockage of urine outflow. By critically evaluating the home you are providing your kitten, you address potential stressors and develop the best environment possible.
There are several components that should be addressed when aiming to enrich the environment:
1) The 'physical system' - are there areas where the cat will feel safe, is there a predictability to it's day, etc,
2) The 'nutritional system' - addressing what and how your cat eats, offering enrichment through toys that allow slow release of food through play, for example,
3) The 'elimination system' - does their litter box allow normal voiding behaviours, do they feel safe while voiding?
4) The 'social system' - this includes all living creatures within the household. Different cats have different preferences for the amount of human contact, and other animals present can be perceived as either a threat, a prey target, or competitor for resources.
5) The 'behavioural system' - the enriched environment allows a kitten to express natural behaviours such as playing, scratching and chewing. By providing approved outlets for these behaviours, destruction of household items can be avoided.
For more detailed information on this topic please visit: https://indoorpet.osu.edu/sites/indoorpet/files/assets/documents/Herron10_EE_for_Indoor_Cats.pdf