Well as mentioned earlier you can always go with the managed VPS solution in case you do not want to deal hassle of maintaining server on your own. This
may or may not include using CPanel.
However if you are not afraid of maintaining your own VPS and have basic knowledge of linux. I would suggest try to use something like "Centminmod". It has
built in wordpress installer and load of option for you. As for the provideR I would say their are many like: ramnode,vultr,digitalocean for unmanaged vps just make
sure they are trusted and have location of server which you want.
As for how many site you can run. This is not something which can be quantified easily. It solely depended on the type of scripts you are running and load on them
you many not be able to host one high traffic website in single VPS if they have high number of concurrent users connecting to vps, but you might be able to run upto
5 to 10 or more wp sites(these are just random numbers) with proper optimization.
I'd suggest:
1. Start with 512Mb ram vps, with 1 core,ssd storage (provided that your provider give you option to upgrade vps easily to higher resources).
2. Try to run one of the websites which you want to move to vps see how it performs and note the resource usage like RAM,CPU utilization.
3. After performing the step 2 you will have a gauge of how much resources your single website consume and that way you can figure out how
many sites you can move to your vps and what resources you need to increase if they are not enough.
Hope this helps.