Welcome to the forums! Take a look at the offers section as hosts aren't allowed to contact you directly. Narrow your list down to a few hosts, and then report back to us for our opinions on said web hosts. Good luck!
I would recommend increasing your budget although I doubt you will have any trouble finding a host that meets your requirments within your budget. Try searching on www.findmyhosting.com or www.hostsearch.com
Hi there BlackKite, welcome to WHT!
I think your spec's are OK, and your budget also a realistic one. You will have no trouble finding a host - but as usual I emphasize the importance of finding an honest and well-reputed company for your hosting needs...
Rather than giving you my own opinions, I suggest you do some research on customer feedback for those hosts you're interested in, then make an informed decision.