A couple of points to mull over. PM or Grizzly, the 1236 gunsmith lathe is usually heavier. That makes a huge difference in the operation of the machine. Ditto for the mill. A 2000 lb mill will run circles around a 400 lb mill. The smaller mill is perfectly capable of doing what you want, but may take 3-4 times as long. You can take much better cuts on the 1236 gunsmith lathe then my1228. Same for a Bridgeport vs my PM30-MV mill. Try to stay with a D1 mount on the lathe or other mount that is more then just screwed on. Then you can run the lathe in reverse. Yes you can run a screw chuck in reverse as many here will point out but there is always the possibility that the chuck can come off. Way too many reasons for running in reverse than to cover here. The light stuff will need more setup and fussing over then an old iron beast but it is a good learning experience. If you decide to go with old Iron, you may need to factor in a 3 phase converter.
As pointed out, if you can get a good quality used machine, then you will like it. However if it needs any work, that could put the brakes on in a hurry. By myself, I couldn't handle fixing the machines, so I bought new. Now with a "decent shop setup" I am looking at bargains to try to restore. Lots of stuff on Craigslist & FB. I am doing Gunsmithing stuff and starting out building steam engines, plus general repairs for a small company.
Money!!
When you buy tooling, really research it. You can get mill boring heads for $25+ all day long. They screw together. I bought mine as a one piece for $ 100. Used it twice in reverse in the last two years and it saved the day. Rotary tables, get one vertical/horizontal with matching tail-stock. When you need it, beats shimming with machinist jack.
Same with mics & measuring equipment. I use Shars & Igauging for everyday use. I can always stay within .002 of everything I want to do. If I want better then that, I use Starett & Mititoyo in a room temperature shop. I cry less on an $30 Igauging DTI dropped on the loor than $150 Best Test.
If you buy a $500 dollar machine or a $10K machine, you will eat up tons of money on tooling. Buy the best at good prices or really good make do at cheaper prices. When you first start out you will need to buy something every time you fire up the machine. It takes awhile before you can just walk up and say I have the stuff to make this. 2 years for me and I am still jumping into the rabbit hole.
Welcome aboard and good luck with your hobby.