VMware Workstation (or even the free VMware Player) is a viable option if you want to run virtual machines on your existing Linux or Windows desktop/laptop. You can then move your VMs to a ESXi server later.
You can run ESX/ESXi/vSphere on bare metal, although (unsupported) you can also actually run ESXi in a virtual machine, for testing purposes. You shouldn't do this unless you already know your way around VMs. I'm a bit overwhelmed with four ESXi instances under ESXi myself. But it's a viable use of a 4 core 16 gig "desktop" for me.
"Which is better" isn't really a viable question to answer based on the existing information in your question.
Pros for XenServer:
- Commercial XenServer (i.e. "Essentials") is less expensive (or was when I deployed it a couple of years ago) than the commercial VMware product suite.
- XenServer integrates with higher-end features of the Citrix Netscaler load balancer (for dynamic provisioning)
- The free XenCenter will let you manage multiple XenServer hosts from a "single pane of glass" as it were (with some limitations). VMware's multiple-host manager requires a paid license as I understand it.
Pros for VMware:
- Expertise in VMware is more common, among both consultants and candidates for hiring. If you need to bring in outside expertise, you can find both, but VMware experts are easier to find.
- More third-party virtualization products integrate with VMware already (Arista's vmtracer, various management and storage platforms, etc)
- Both have a free version. It can be used in "production" but you will likely need to upgrade to a commercial feature if you want high availability, VM migration (XenMotion/VMotion), storage migration, and other high-end features.
- At a very basic level, either will probably do what you need, but you may want more or different features.
As an aside, Xen Desktop probably isn't applicable to this discussion... it's a virtual desktop platform, so you can effectively use a thin client and your applications/OS can run on a server. It's analogous to VMware View and ACE.