As with all things SharePoint, the answer is: It Depends.
Depending on the size of your organization, your DBAs can handle the management of the SQL and the server team can manage the hardware/OS. While these seem like meta areas, they are essential to SharePoint operations. An improperly managed/patched database server can kill SharePoint. Likewise, underpowered or aggressively shared hardware/virtual machines will also kill performance. If you are going live in SharePoint 2010, these are even more important.
As to SharePoint itself, you will need a SharePoint Admin. This requires an understanding of the SharePoint technologies, the SharePoint infrastructure, IIS, the http protocol, asp.net infrastructure - especially the caching options, Windows Server, solution management, enterprise search, Backup/restore strategies, Active Directory, DNS, Powershell, knowledge of Third-Party SharePoint tools like Quest or DocAve.
From what I'm hearing from other companies, qualified SharePoint admins are very hard to find and it is usually better to take an existing Windows Server admin who has an interest in SharePoint and train them on the high level aspects of SharePoint.
You will also need a front-end support person that can walk the average user through the basics of SharePoint - uploading files, check in/check out, publishing, etc. easy stuff.
You will also need a Business Analyst with a deep understanding of the OOB components in SharePoint to help your business users leverage the tools available. The business will most assuredly have requirements beyond the average user, and this person will be the first point of contact for that. They will also be the ones to raise the flags early if perhaps a custom solution is needed.
If you plan on writing custom solutions for SharePoint then you will also need a SharePoint Architect. The skills required for this are a combination of SharePoint Admin, Business Analyst and SharePoint developer. You need someone with experience because a poorly designed custom solution can not only make your SharePoint environment unmanageable, but it can also cripple performance. Initially, a SharePoint Architect can also fill the SharePoint Admin role but you will eventually need a dedicated Admin as the Architect's time gets stretched thin quickly.
As you no doubt have already seen from your training so far, SharePoint is not something you can 'pick up' in a month or two. It has a learning curve measured in years - just for Development.
Since you are just getting started, I would STRONGLY advise that you plan out your environment. Not just the hardware/software aspect but also the business needs and goals and mapping how SharePoint will be used to address those. Unregulated/unplanned SharePoint installations have a nasty tendency of growing like weeds and filling up with all sorts of unwanted garbage, making future upgrades a nightmare of epic proportions. Failing to plan now will result in a substantial increase in costs later on. Microsoft has a lot of good documentation on this.