300MB "if" you really have that should be plenty, my understanding is that mosts hosts like Arvixe provide 200MB which also should be enough.
If you are deploying a build you made from source code make sure you are doing a release build not a debug build and make sure that in the deployed web.config file that you have <compilation debug="false"
a debug build will use much more resources than a release build.
If you have custom features that you are deploying consider what they are doing and how much memory may be used by your custom features.
Also review what kind of errors you are getting in the mojoportal log.