Congrats. Now that you've got the old barrel out.....a word about installing the new barrel. First, check the threads on both the new barrel and the receiver. Especially the receiver. Unfortunately, the old technique of fitting Mauser barrels with a "crush fit" tends to damage the receiver threads (compresses or "crushes" them). "Crush fit" is a bloody STUPID technique - period. Ignorance, plain and simple.
The reason you are having trouble in screwing the new barrel into the receiver is probably that the threads are damaged. You MAY need to obtain a suitably sized thread chaser and work over the receiver threads. After checking everything carefully, try this first: heavily lube the barrel threads (even a thin grease for this purpose will work)....then slowly screw it into the receiver, a bit at a time, under more than hand pressure. Stop often, when it hangs up and back it out. Check for any debris or bits of shaved metal, etc....clean, re-lube, then try it again. Working this way, you MAY be able to chase the receiver threads, by using the BARREL threads. Understand, this is to chase the receiver threads....and get the barrel TEST fitted. It is NOT final fitting of the barrel - so, if you get it all the way in this way, DON'T just torque it down and decide that you are finished. This technique MAY not work - if the threads are too buggered. If they are, then a thread chaser or actual re-threading may be needed. BE CAREFUL - if your receiver threads are too damaged, you could damage your barrel threads to match - not a good thing.
Once the issue with the threads is solved.....let me say this about the final install of the new barrel. PLEASE DO NOT do the stupid "crush fit" technique ! It is both unnecessary and will simply cause the same problem all over again. The new barrel only needs around 75 lb/ft. or so, of torque. (The barrel will not "shoot loose" with this much torque.) What you want, for good tight headspace, is to ensure that the barrel face bottoms on the inner torque ring. There is NO need for the outer barrel torque shoulder to contact the receiver face, before that is achieved. That is what produces the "crush fit". So, for god's sake, cut the outer barrel torque shoulder back enough (or the face of the receiver) so that they only barely touch, when the barrel is torqued in place. Then, damage to the threads will be avoided - and future re-barreling will be easy, as it should be.