Speaking as someone who rents a server I can only tell you that the terms "huge database" and "cheap" don't go hand in hand and I am sure others such as Alex will attest to this as well. The very reason I run a private site is because if I were to make the it public I would not be able to afford to run it for more then 1 month out of the year and it would not really be worth it but if you are commited to the idea then I suggest you got to
http://webhostingtalk.com and ask some of the people over there where you could get the best deal because most of the members there run their own servers and thus very knowledgeable about this topic and good luck.