Neil said it right - it's recommended to give users as many permissions / privileges as they actually need or have to. It is very likely that for this person the Manager user group would be sufficient, If for example you only want this person to be dealing with content.
However, your needs may be different - so keep in mind that you can always create custom ACL in Joomla, with your own Usergroups and View Access Levels.
But I wouldn't recommend to start messing with those on your live site, especially if you have not previous experience. You could experiment on a testing environment to see how it works, and how you could setup your own ACL.
For example, you can have special access permissions on components, modules, menu items, categories, articles.
In addition there are other 3rd party extensions that give even more options and capabilities, like building a custom admin menu for your backend users... - you could check at JED for this.
JCE and Editors
Joomla allows per user Editor assignment. So you can assign to your users the desired Editor.
Now JCE itself, comes with profiles. You create JCE profiles that contain predefined set of features and permissions and you can assign those profiles to users, usergroups among other assignment options.
So, you can create a simplified JCE profile, that will have only the interface and JCE plugins you want to allow, plus some obvious restrictions like inserting php, js etc, and you can assign this profile to your users.
Update for your comment on your own question:
Here you can read more regarding Joomla ACL and the default usergroups:
- User Group/Access Levels
- Joomla ACL
Note that in the first link, you will read that administrators are allowed to perform installations, but this is not actually true for the recent Joomla versions. Administrator don't get access to the Installer component, so the part of your question if an administrator can upload and install server-side scripts is covered.
However, the exact level of permissions and access you want to give to this user is up to you. As described earlier in my answer, you can create a customized ACL for this user, allowing him only certain access. Use also JCE's profiles, to give him certain abilities when writing content - so for example don't allow him to write php, js inside the articles, restrict him on the html elements he can use or the files formats he is able to upload. All these are up to you to decide how much you trust this person and what you want him to do in your site.