you said you are a home user , are you setting up a lab for study ? if so , why not use evaluation or better vmware's cloud cred
Regarding your CPU core concerns, you can over commit CPU cores, so if your host (microserver) only has 4 cores, you can actually have VMs running on it happily with say a total of 6 cores, providing they are not all needed 100% of the physical CPU resource (measured in GHz) You don't "really" know what cores are being used by what VMs unless you dig deeper, ESXi deals with that for you. Just keep an eye on the CPU performance settings on the physical host.
As for the web client, yes you will need vCenter to use this (free on a 60 day trial) but if this is just a basic home lab and you just need basic features then your vSphere C# client will work fine for all VM features up to hardware version 8.
VMware have some very good HAnds On Labs if you want to take a look at things without a ab / wanting to install vCenter etc: VMware Learning Platform
As for remote access, you could use the port forwarding approach with the C# client and / or web client, (They both use ports to communicate over the LAN of course) I wouldn't advise this though unless you have adequate security in place ie using a secure VPN.