Just get your router sorted and run from home if this is your first server. Running a mir server to a reasonably high standard can be a time consuming and difficult task. You should try it at home before you dive into dedi servers, before you know if your server will be popular.
However:
For a nice server, with decent specs that can run mir, and a decent connection to the net, with tech support, you're looking at £70 a month, and £50 setup fee, and 1 month up front, so £120-150 upfront, and £70-90 a month.
Donations will be hard to come by when your server is new, even on a dedi server, players are not going to assume that this means you are going to be online 2-3 years.
Getting the net connection right is a big thing too, most servers will give you an allotted bandwith. Which means if you're running your website, with client and patches on there, and your server, you could run up some hefty bandwith bills ontop. Example, i did have my client on my site for a few months, i opened it for download, 1 week out of every month. My bandwith was aprox 80-100 GB a month.
Plus stay away from american servers (the links on here), you may save some money, but think about trying to contact them by phone to solve a problem asap.. Plus the speed of the server will suffer due to the high distance from the UK.
You will also need alot of technical knowlage about how windows server and ISS works to run your site and server. Because the techi support will not cover you usually for general running.
I feel i've been quite negitive, so i'd like to say there is a huge upside to having a dedi server, and thats piece of mind that it will stay onlin 99% of the time. Its power to run a mir server in its sleep. Full root access which means connection via RDC, so you have full control. Ability to run a site with all the extra's such as CGI, ASP, PHP ect. Fast internet connection speeds and the ability to play your server without the aid of another PC (as running it at home would require another PC).
What you should be looking for is a 2GHz+ CPU (CPU power does not need to be great, infact a 1.5GHz CPU will do). 512Mb RAM minimum, 1024Mb reccomended. Net with at least a 10Mb upload speed(high download speeds are not really needed to run the server.), although upto 30Mb would be desirable to allow client dowloads as well as the server running. You don't need a huge HDD, my mir server only takes up about 2.5Gb with 16 months worth of log files, backups and tools to run my server. And it needs to be a windows OS. Windows 2k3 WebEdition will run it fine, but Standard will manage the memory alot better.
Hope i've been some help. Good luck with your server.