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/Peo, FreeWebSpace.net
Dont think you will find a dedicated for that budget. If you definitely need access to the whole server for whatever reason then check out: http://www.serverpronto.com
Otherwise, I think you are probably more suited for a VPS. Good luck!
For that budget, VPS would match your request better.
Here is what we propose you although you posted no specs.. I recommend you check out our full line of VPS packages.
Intermediate A VPS
256 MB Guaranteed RAM
512 MB Burstable RAM
20 GB Disk Space
300 GB of Premium Bandwidth
HyperVM VPS PowerPanel
2 IP Addresses
Choice of Operating System DirectAdmin Included $39.95 monthly Order Here
Virtual Memory (RAM) - 256 MB
Processes - 120
Dedicated IPs - 3
Included - VPS Admin Panel, CP+ (30 Day Free Trial), Complete SSH Root Access, Install & Run Your Own Applications, Manage Own Config Files, Complete Independence, Own Network Configuration & Routing Tables, Full Control Over Files & Processes, Virtual Ethernet, Own Hostname, Configure Own DNS Servers, Pre-Installed Services (Mysql Apache Bind vsftpd & proftpd).
Included Upon Request - Webmin, Usermin & Virtualmin.
If interested send PM.
Note: The plan can be customized depending on your requirement.