You should use -p flag so as to count fragments. Don't use -M flag since you don't want to count multi-mapped reads. Use -t to count at exon level but summarize the counts per gene identifier using -g. If your library was stranded you will want to use appropriate -s option (most likely 2). Provide all BAM files (in the order that you want the columns to be in) in a single command to get read matrix. Your BAM files can be sorted or unsorted. If they are unsorted then featureCounts will sort them on the fly.

Here is a summary of possible command lines.

In future, you could use STAR itself to generate the counts.