What a good question you pose! Differences in personality and degrees of autism have an enormous bearing on the answer. [We have a daughter, now grown, with autism and developmental challenges, so I can relate to some degree to the difficulty in finding a workable approach.]
For the vast majority of children, phonics is hands-down the best approach to reading, for phonics gives children the tools to decode most words, particularly those that they don't immediately recognize. Having said that, however, a tiny percentage of children, with exceptionally strong visual memorization skills, may learn more easily with sight reading. Our dear daughter is very low functioning in logic and reasoning skills, but she can almost immediately memorize anything she sees. [She knows exactly where everything in the house is at any given moment, from potato peelers to safety pins, what time the sun will set today, and which day of the week every family members' birthday falls.]
Our daughter also balked at anything new or perceived to be difficult; that characteristic has not changed with age so, in her case, waiting until she was older to introduce something did not help.
What did help in her case was to give her plenty of lead time to transition to something different. For example, if we said that it was time to dress for church, she would fall apart. But if we told her that in fifteen minutes, when the timer went off, it would be time to dress for church, she had time to accept what was coming. Often, with the heads up, she would begin to dress sooner, just because she knew that she had some choice in when she began. Perhaps if it is announced that we'll have a new word game after lunch, your son might be better able to make the transition if that is a problem.
In any event it is good to teach phonics so that your son can sound words out, but the emphasis could be put on teaching sight words if that seems easier for him. In either case, teaching the word families introduced in Little Stories for Little Folks is a good beginning. Because of your son's unique needs, I'll offer several suggestions that could be tried.
If he has started the LSLF booklets but balks, it might be good to give him a break from reading books, and instead put the focus on either sounding out words from the same families, or memorizing them, depending on which approach seems better suited to his abilities.
A very simple way to foster success with word families is to make the following game. Print the letters at, from LSLF Level 1, Book 1, on two index cards. Leave enough space in front of the first letter that another letter can be added in front. Then print b,c,f,h,m,p,r, and s on a few other cards. These letters are then cut out as 'tiles,' leaving almost no margin on the right side, so the letters can be placed right next to the at on the other index cards. Now put the cut out tiles in a pile in the center of the table, and give your son one at index card while you take the other. Tell him that you are going to play a game. First, you pick a tile and make a word by placing it next to the at on your index card. Then he does the same thing. Taking turns, each player forms a word. Sound out your word slowly, and help him sound out his word if he needs help. Praise him mightily with each word he forms and, if he particularly likes almonds, raisins, or chocolate chips, award one treat for each word formed. [Have him wait to eat them until the 'round' is finished, so he can see a little pile form.]
If he tolerates this game well, play it once more, but with this variation. Have him begin, and let him have as many turns as he needs to form all the words he can find. Again, praise and award a tiny treat for each word. Tell him that his turn is first, and you will take a turn when he is done. If he successfully uses all the tiles to form all possible words, tell him that he got all the words before you, so he won!
If this approach meets with some success, wait until he can easily sound out or recognize the words from that family, and then introduce the next family from LSLF Level 1, Book 1. When he can easily read words introduced in that booklet, move to the next. [Don't read the booklet itself yet.]
If [or when] he has made it to Level 1, Book 6, he might benefit from playing the 'Silly Willy Sentences Game' included in the LSLF program. The game will also allow him to practice reading in a fun way.
Finally, when he is comfortable reading words from all the word families up to Book 6, he might be willing to read or return to the stories themselves up to that point.
Another approach is to read with him, taking turns. Mom reads the first sentence; son reads the next and so on.
Whichever approach is selected, it would be good to keep sessions very short at first, perhaps five minutes. As your son relaxes and begins to enjoy the sessions, they can gradually be extended. Praise every effort and success.
May the Holy Spirit guide you as you educate your son for eternity--you are in our prayers!