What bottom bracket do I need? It measures 67.5 by 39/35mm?

Bottom brackets are sold to match the crank you buy, there is usually a recommendation for spindle length. It is going to be difficult to buy crank and bottom bracket as well as a saddle and grips withing your budget. To replace your bottom bracket you have to remove both cups from the frame, it isn't clear from your question whether you removed the right hand side. When you remove it, if it is left hand threaded, your bottom bracket is English threading, so that is what you will have to buy.