Definitely agree on replacing cleans with more targeted movements -- slight nitpick, none of this is "weightlifting" which is a separate sport of its own requiring these movements but incorporating power and speed to efficiently perform the snatch and clean and jerk with maximal load on the bar.

One thing to keep in mind with starting strength is that it was meant for high school football players who needed to rapidly add mass and strength. Low bar squats emphasize the posterior chain which are simply larger muscles, and will help the beginner see bigger gains faster and without spending time on the particular advanced cues necessary to perform high-bar squats correctly and safely without injuring your joints. (I'm thinking particularly of adductor strength and thoracic spine mobility.) On the other hand the low-bar squat is often coached incorrectly , resulting in much worse stress on the back and elbows (terrible cues like "knees back", etc). When taught correctly, the pressure commonly felt in the shoulders and elbows in this lift is simply a lack of flexibility and will resolve itself.