Before you get a dedicated server, make sure you have a program worthy of running on such a server. What I mean is, in order to drop catch, you will need to either build or have built a program that is capable of catching domain names and it will take time to perfect the program with trial and error.
Do all your testing from your home machine and once your happy with your program then you can start thinking about moving on with a dedicated server. There is no point in having a (potentially) fast car with no engine.
Hope this helps.