For straight virtualization I would suggest VMWare: ESXi is free if you don't need any of the advanced features (high availability, cluster management, etc.), and if you need those features VMWare has them developed, tested & supported, which IMHO is totally worth the licensing and support fees.
As an added bonus VMWare virtualization looks like physical hardware to the OS, so your "future provider" won't have to worry about any strangeness/"virtualization leakage" that can be introduced by other technologies.
As far as actually getting your systems into the virtual environment, VMware supplies the VMWare Converter tools to simplify direct Physical-to-Virtual migrations, but a virtualization project is a great time to look at your system architecture and determine if there are any changes you would like to make.
Re: your project as described above, was this just dumped into your lap or do you have some guidance/help from above? Generally speaking I wouldn't consider virtualizing an environment as a task for a "trainee"(intern, jr. admin, etc.) unless they were getting some help in the process.
Among the stuff you mentioned above, picking hardware is particularly important (getting an idea of the kind of disk bandwidth you'll need, how much RAM you'll need, what the CPU load is going to look like and whether or not reservations should be made for specific machines/classes of machines (i.e. configuring "resource pools" in VMWare's terms).
Getting that kind of stuff right is especially important if you intend this hardware to live out its entire useful life cycle while still providing what your clients would consider good performance, and just going based on the fact that you're a "trainee" I would suggest working with someone familiar with your environment who has the experience doing profiling & the instincts to spot performance bottlenecks so you don't wind up with any unanticipated problems.