I agree, there are lots of advantages of having full control over a server, that you would not get from a low cost hosting option. There are database connections that you only get limited control over with low cost hosting, read/write and execute permissions are also much easier if you have full server access (dependent on OS system), + installing software is much simpler if the server is next to you. (these are just a few reasons and im sure there are also a 100 and one other good reasons to have your own local test server, not to mention speed).
This said, it all depends on what you are to use the server for, if this is for your "first" web site and you have little to no coding experience, low cost hosting would probably be perfect. However if you are an advanced coder (or learning to be, or a wannabe server technician) a local test server may be useful.
Power wise, i don't feel this is important if you are only using it for Dev work, you would be fine with the minimum OS requirements and possibly a little more RAM.
If you are to also use this server to work on and run your development applications, how powerful it is depends on how fast you like your PCs to perform for you.
If you are simply going to transfer your code to this server to test it, as i say i don't think power is an issue.
Servers only need to be powerful if you are expecting 1000's (or many, many more) people to connect to it at any one time. Or if you plan to use very large databases / large and complex coding. Typically the average website does not tax most modern servers. I have seen people buy dedicated machines, but only use a very small %age of their total power.
If i were you i would save your money and buy lower cost older components or dig out an old machine and test install an OS to it. (from what you have wrote i would say anything over a P4 with 2 GB of ram would do the job, unless you have money to burn).
Hope this helps.
Jon
EDIT / P.S if you are using it for IP cams, RAM and a largish HDD would help (and maybe a little more power than a P4 if you want to run more than a couple of cam feeds at a time)