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I have used Arvixe for two years, and they are the BEST budget hosting provider in my opinion, a lot better than companies like Crazy Domains. They have 24/7 live chat on their website, and most of their packages already come with a free domain name. I highly recommend their Linux hosting plans, I currently have a reseller account with them, that I use to host all of my websites, as well as my family's.
Personal Class - $30 per year (with coupon) - unlimited disk space and bandwidth (in accordance to AUP), can host 6 domains on the account
Personal Class Pro - $48 per year (with coupon) - unlimited disk space and bandwidth (in accordance to AUP), unlimited domains (I have hosted around 10 domains on one of these accounts before, without any issues)
Business plans:
http://www.arvixe.com/business_web_hosting
Reseller plans:
http://www.arvixe.com/reseller_web_hosting
VPS plans:
http://www.arvixe.com/vps_virtual_private_servers_hosting
Can web applications hosted initiate outbound connections?
For example, could I host an app that in turn calls some external webservices to lookup data from various sources?