Managed VPS generally comes with cPanel.
You have a decent budget. Check VPS offer section and short list few providers. And then search for their reviews on WHT and Google.
Check tmzvps.com they may fit your requirement.
█ YagHost - Pure SSD Hosting | Since 2007 | Average Response Time: 15 min
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█ LopHost.com - Web Hosting Tutorials
Your price is on the low side, regarding managed VPS node, but there is a chance.
If you drop the management requirement and learn how to manage it yourself (there are many tutorials available) you can save some bucks and get a better node.