Hardware requirements will vary depending on the volume of users you anticipate will access your cBioPortal instance and the amount of data loaded in the portal. We run cbioportal.org on an AWS r5.xlarge instance with 32 GB and 4 vCPUs. The public database consumes ~50 GB of disk space. The site is visited by several thousands of users a day. For on-premise installation recommendations one can look at the AWS instance type specs:
The hardware requirements are much lower when one has only a few users a day. Minimally, 2GB of RAM is needed to run a cBioPortal instance. If you do not plan to import public studies, depending on the size of your private data, 10GB of disk space may be sufficient.