Students often face this question in determining the best semester to apply for. Typically, highest acceptance rates are for the Fall semester. Fall has always been the semester for the highest intake of students at most universities. Fall semester provides a seamless transition from one degree to another as well (with no time lag in between). Departments admit more students compared to other semesters. Universities and departments usually have more funding (makes sense as it is the start of the fiscal year). More number of assistantships, student worker jobs etc are assigned in Fall.
Summer is an odd semester to start with. Several universities do not even accept students or offer courses during this semester. Most universities has reduced course offerings in this semester.
Spring should be, in my opinion, the second choice. Delays in applying or visa/admission rejections or late decisions are some of the reasons to have missed out on the Fall semester.
However, international students are very wary of H visa limitations. Depending on the course of study, one can determine the semester of graduation. Students apply for H visas in April of every year. With the number limitations, this process is now a lottery. So, choosing the right semester to start or graduate might provide more number of chances at applying for the visa.