As you say it is a skill that worth your while to learn. Single speed wheelsets are the easiest to build and the internet/wheelbuilding thread is always there to help out. You'll probably be going over your reserved budget if you go down that road
I think a chain catcher might be the cheapest option cause with a clutch mech you'll also need the appropriate shifter. Not sure... You can try the 'Any questions answered' thread for a definite answer
As you say it is a skill that worth your while to learn. Single speed wheelsets are the easiest to build and the internet/wheelbuilding thread is always there to help out. You'll probably be going over your reserved budget if you go down that road