When there are many MSG files converting them one by one is not a good idea. It takes time and attachments can easily get missed if the process is not handled properly. First, keep all MSG files in one folder and make a backup copy before starting.
For this type of work you can try a trusted platform WholeClear MSG to PDF Converter. It supports batch conversion so multiple MSG files can be exported to PDF in one round. It also keeps email details like To, CC, BCC , From, Subject and Sent date. The original MSG files are not changed during conversion. Attachments are exported into a separate folder which makes review easier later.
A better idea is to test the free demo first with a small MSG folder. It helps confirm the PDF output, email headers and attachment saving before using the full version.