0-6 months
Toys: YOU are their favorite thing to play with for the first 3 months. Between 3-6 months you can introduce rattles, soft books, sensory toys (things they can reach for, hold, shake, make noise, suck on), soft plush toys and dolls (with no little pieces that can detach themselves), crib mobiles, teething toys, stationary activity centers, and playmats.
Play Ideas: Spend time with your child face to face playing tickle games and making silly faces/sounds. Take a soft plush toy and rub it against different parts of their body/face so that they get that tactile stimulation and feel the soft texture. You can also take their hand and have them pet the stuffed animal. You can take some rattles and practice shaking them then stop and see if your child reacts when the noise ends and engages you to continue. For example, you can practice having your child make eye contact to request more rattle shaking.
6-9 months
Toys: You can introduce cloth/boardbooks, toys to manipulate (poke, twist, squeeze, shake, drop, open), lightweight ball (for rolling), kitchen items (plastic cups, wooden spoons, spatulas, plastic bowls), toys that make noise when baby does an action (be mindful of loudness levels), toys that can be pushed (animals/cars on big wheels) and large balls.
Play Ideas: Your child will start to imitate gestures at this age so you can play by making simple movements that your child can imitate and imitate their movements as well. You can play with toys and then hide them out of the child’s view to see if they realize the toy is missing. Have the toy disappear and re-appear a few times. You can even just throw or roll an object away and see if your child follows the object with his/her eyes.