You'd be set for machines with the Bridgeport and SB lathe. Definitely would want a rotary table too. I used a dividing head with a chuck for some of the machining also.
To answer you question directly, the project does not contain any what I'd call extremely difficult to machine parts. I am a beginner also and learned a ton making my gun (still not quite complete, will make a tripod this summer). I've run around 400 rounds through mine.
By the way, there are at least two dozen errors in the drawings. No way, no how the gun will fire if made exactly to plans. I had a text file somewhere on the computer summarizing the errors, got the list from this forum. I found another dozen errors as my build progressed.
Be prepared to spend a couple of years also. Paul estimates around 600 hours to make a gun. I'm probably a little short of that.
I'd recommend barrels from Dave Burnett whose on this forum. I bought 10 used Ruger 10-22 barrels off from him for under $200. I also varied from the bolt diameter/carrier block bolt diameter. The plans call out a 0.420" hole which when I checked for a ream found one for $85 from Enco. I went with 9/32" instead (0.4218") for about $15. Changed the lead angle on the extractors from 15 deg. to 45 also. Could keep going on and on . . .
Don't be afraid to jump in. You'll likely end up making some parts 3 times in the learning process. But what the heck, you'll gain a lot of skills and confidence in your abilities! Plus, maybe ammo will be under $0.10 per round by the time you're finished! My biggest issue was getting good silver solder joints (still working on it).
Don't hesitate to email me (not that I'm any authority or anything), but I have a working gun so must have done something right! Be prepared to make a number of fixtures for the bolt construction. I made 5 or 6 simple fixtures so they are all interchangeable.
Best regards, Bruce