It's not good to take a fresh rebuild for a long ''first'' ride. It should be taken out for 15 minute short rides and cooled off. Now you need to take it out for a 15 minute ride, come home and dump the oil and put fresh 4 stroke M/C oil in. Ride it easy don't run it full throttle just yet. Change the oil frequently! You are going to see a lot of fine metal in the oil, don't panic. You have to change it often in the beginning. 4 speed CT70 engines are not easy to find, and if you do they are going to run you some big bucks.. $1000.00+ easy, if it's rebuilt already.
If you are buying a used core engine it will cost around 800 bucks in parts, plus whatever you pay for the piece of crap. Consider buying a ''basic'' 88cc kit, that's close to $150 and a $150 4 speed AHP transmission + a $165 trailbikes 4 speed manual conversion kit. That's $465.00 worth of shit right there to add on to all the money you already dumped in to it. Don't buy someone else's used headache. Build your engine up.