Instead of looking to your budget, you may just find out a web host that holds the entire features which you have listed. You may have a look at Web Hosting India. I feel that you will be better satisfied with their hosting plans...
There are some not so big box companies with excellent prices for VPS. The big names have too many clients to serve in my opinion. The prices might be lower but usually you pay a bigger price anyway when it comes to customer and technical support. Look at some reviews. Maybe even go for an A- list or a B+ those are the providers who know if they don't stay at the top of their games they will be dragged down to a level where they can't survive. Hit the up and coming review list but make sure the provider has some longevity.
Unixy.net is awesome. Check out my site @ www.47r-squad.com They support all third party plugins. Their cPanel Varnish is awesomeness Check this thread out at WHT: http://www.webhostingtalk.com/showthread.php?t=1017369