welcome in the VMware world ;-)
>Most of all, it`s being said vCenter is best to be a VM. Then I see ESXi being installed after vCenter is operational, and being added to the console. Now, this looks like a chicken-egg problem to me. Which came first for god sake? 
//I guess you have checked that all of your hardware is compatible
Install your ESXi and configure it probably (network, DNS, NTP, storage-connectivity). Create your datastores and install in this ESXi your vCenter VM (vCenter appliance or the windows installation). In certain cases you want to split services like SSO, Inventory-Service, WEb Client on several machines.
Decide which database you are going to use for the vCenter (internal (supported up to 5 ESXi-hosts) or external (oracle,microsoft,ibm...)).
After you have installed/configured your vcenter you can connect to it and attach all of your ESXi hosts to it and configure the rest probably (manually or with host profiles).
This is just a short overview of what to configure. You need to consider design basics as well (which cluster, networking, datastore size, VM deployment processes, certificates....there a lot of good books out there (e.g. a good start is vSphere Design by Scott Lowe, et al.even though it written for vSphere 4.x )
You should definitly read the VMware installation guide here:
http://pubs.vmware.com/vsphere-51/topic/com.vmware.ICbase/PDF/vsphere-esxi-vcenter-server-51-installation-setup-guide.pdf
If you have existing VMs running in other vSphere environments, you can add them by making the storage "accessible" to the new ESXi host and register them to your new ESXi hosts. (e.g. add the old ESXI to your vCenter and migrate datastore&hosts) or by export and importing the old VMs as OVF files.
For myself, I prefer to keep the exisiting VMs if they were running on an ESXi before, instead of new installation. But of course the depends on the complexity of the Applications and their migrations process.