Mike, you have educated yourself quite well for a newbie, I am in awe. A few comments and questions:
SOME new parts are available for Logans, but they are pricey. Used parts are often available for most lathes, except for the one you need really bad and right away.
Imports all look the same, but they are built in many factories to the same designs, and many of the parts are made in small shops, some in garage size shops, and then brought together to become a lathe. Although they might look all the same except for the paint color, often seemingly interchangeable parts when held at hand's length will not quite fit another "brand" of Chinese lathe, or ones they made a few years before. Sometimes they can be made to fit. That is not really a problem. The castings do not often fail. Many parts can be made by the machinist. Some are standard hardware.
Is your 5' x 2' size critical? I think I could see you with something like a 12x36" lathe, which are capable of a large range of work but might be a bit larger than your stated limit. Older lathes often do not have adequate high speeds, especially for using carbide tooling. On something like a 12x36, I would be looking for a high speed of at least 1500, and 2000 is better. A ball bearing spindle is needed to reach those speeds. Low speeds are just as important. Mine goes to 70 rpm, but that is sometimes not really low enough, though it can be worked with. I would prefer a low end down to around 36 to 45 rpm on my 13x40 lathe. Smaller lathes are often limited from doing large work more by limited low speeds than by the lathe capacity. You will very soon want a QCTP. Do not dismiss 3 phase machines out of hand. With a VFD (~$200) you can run the lathe off single phase and also have variable speed control at the same time, and some other benefits as well. Often if you can tweak the speed a bit you can stop chatter, and/or improve surface finish. Speeds can also be extended to some extent with a VFD, but there are some caveats to that. You will want a 4 jaw independent and a 3 jaw scroll (self centering) chuck to start out with. That is pretty standard stuff.
You are new to lathes. If you are looking at used lathes, I highly recommend finding a knowledgeable and experienced person to help you inspect and evaluate them. A real dog looks about the same as a real score to someone who does not know what to look for. Some help might be good for choosing a new lathe as well. Buying tooling is expensive, figure that into whatever you buy and what it comes with.
Lastly, do not get in a hurry. Take your time and make sure you get what you want for what you want to pay, and in a condition that will not sour you on machining. Patience is a required virtue here. You are definitely on the right track...
HAVE FUN! And keep us posted...