Look for toys that stimulate their senses. Many autistic children have sensory challenges, particularly tactile defensiveness. Toys can be an excellent way to introduce tactile sensations in a low-key, non-threatening way, in which they have total control. Suitable toys might include:
Books with cloth, foil, yarn, etc. attached to them—you can even make your own
Blocks with raised lettering or numbers (this appeals to the ordering need as well)
Toys with bumps, fur, raised elements, ridges, etc.
Musical toys and toys that make sounds
Hard board books for children prone to tearing - allow them to tear the wrapping paper as much as they wish!
Choose toys that help social interaction development. Teaching all children cooperation through toys is an important rite of growing up. For autistic children, socially interactive toys are even more important for helping them to develop coping mechanisms when interacting with the wider world. Board games are excellent for this, especially when the whole family pitches in to play together. Focus especially on the issue of taking turns and that losing is not a big deal. All children need to learn these skills but the frustration element can be very intense for autistic children.
Find toys that help to develop motor skills. All children need to develop motor skills, but autistic children are especially likely to struggle in this regard. Painting and drawing are good choices, and trying fingerpainting can help sensory issues (if the child is able to try it). Developing balance might be tricky if the child refuses to ride a tricycle or bicycle. A lot of encouragement and patience will be required, as well as understanding that it might never happen. Trampolines are excellent but make sure it is safe and always be present.
Consider toys that emphasize or provide room for organizational skills.Functional play does not only help the child with their weaknesses; it also encourages them to build upon their strengths. Autistic children are often skilled at creating and understanding systems. You can encourage this by buying toys that allow them to design cars, construct elaborate towns for their dolls, and employ their visual skills. It may inspire them to go into STEM at an older age. Look for...
Toys that can be taken apart and reassembled in different ways
Puzzles and brain games
Dollhouses or toy towns to organize
Buttons and beads (consider choking hazards)
Always be considerate of the child's skill levels. Less complicated toys are better for younger children or ones with greater sensory or intellectual impairments; simple push-button, open and use toys are best. For children with stronger skills, building, creating, discovering, connecting, etc. toys are generally fine.
Don't overdo the functional play. Sometimes, it is fine to let your child simply enjoy a line of toys that is pure fun.
Remember that there is no "correct" way to play. The point of playtime is to have fun and relax—not to behave exactly like other people want you to. Allow your child to be themselves. It's okay if their playtime looks a little different from that of other children.