Sounds like your doing a great job with him and his home ! Yeah your going to need a heater and that should come first, its getting cooler where I live in Tennessee and I have noticed my heater is starting to come on more now. Also get a themometer to check the temp of the water and keep and eye on the temp as the tank water starts to heat up to make sure its working alright. I have and Elite adjustable heater its doing a great job, I have mine set to 78.
About the difference in the worms I am not sure but I believe the blood worms are safer and there might be some issues with the black worms if I am remembering correctly some people here have said not to use them. I know you can get the frozen blood worms, they come in cubes that you slice a piece off of and let them defrost some and then give them to your Betta, I think most people here use those. They are better cause you dont have to worry about any germs being on t hem as they have been frozen.
Hey some live plants that float would be nice if you want something that floats at the surface of the water, I have Hornwort and love it and so does my Betta Perseus although he attacked it when I first put in the tank...lol