You can allow your kitten the run of the house but keep several litterboxes close by. Using Dr. Elsley's Kitten Attract Litter should also help entice kittens to start using their new litter boxes. Make sure the sides of the litterbox is not too high for your 8 week kitten. Over time, after a month or so, you can slowly switch out this litter to an all natural litter. Also, over time you can slowly move the litter boxes from their close but inconvenient places to their permanent places and even decrease the number of litter boxes as the kitten learns their new home and learn to hold their waste longer. If littebox problems persist then you can adopt approach Two.
Most literature online refers to approach two. You start the kitten off with a small area and work your way to big. So keep the kitten in a bathroom or small bedroom where they can learn the lay of the land and always be close to a litterbox. If at any point in increasing the area the kitten roams that litterbox problems creep up again you can either decrease the area again and wait for maturity or increase the litterboxes and go back to Kitten Attract litter.
Do expect your kitten's nails to be out more often as they don't learn to sheath them until they're 4-5 months old. A kitten's nails serve as a protective mechanism while they are still young. You can curb this issue by trimming the nails every 7-14 days.
Want to sleep with your kitten?
Cats are by nature nocturnal animals. This means that they want to be up all night and sleep all day. Since we are on the opposite schedule, cats try to adapt to us by being awake during the day to be with us but require frequent and long cat naps. Cats can learn to sleep with us at night but sometimes requiring training. You can have a cat bed next to your bed or on your bed that is a dedicated spot for your kitten. Following a bedtime routine, just like for kids, will help a kitten prepare for bedtime. We even tell our kittens "Bedtime!" before turning out the lights. If a kitten wakes you up at night because they want to be active, kick them out of the bedroom. Since cats are social and love to co-sleep, this serves as a time out that will teach them quickly that waking you up is not acceptable. Do keep in mind that you will need to allow the kitten a way to access a litterbox as they will probably not be able to last throughout the night without relieving themselves. As I mentioned before, it's not in a cat's nature to sleep the whole night and will have to develop the ability to hold off using the litterbox for longer than normal times. When you first get your kitten at 8 weeks, they may not even be able to sleep with you at night immediately because they may sleep so deeply that they will urinate in their sleep. The only way to know is to try it and then if it doesn't work, hold off and try again when more maturity is reached.
Lastly, I can't express enough how helpful having a comfort zone diffuser installed 2 weeks prior to your kitten's arrival is. This will make a stressful life change into a more manageable and quicker transition.