Read the HSS grinding model tools thread. It's long, but there is a ton of great info in there for new machinists. Even if you don't make HSS tools. The discussion around cutting forces helps with understanding why tools are shaped the way they are and how to use them to get the results you want.
My PM1127 didn't come with a tailstock drill chuck. Consider that required equipment if it doesn't come with it. I hear the PM Precision chuck is good, Albrecht is kind of the gold standard, but not really affordable new for hobby guys. I have one from Glacern and have been very happy with it.
One thing I really like on the 1127 over the 10x lathes from PM is the camlock chuck. The 10x uses a bolt on chuck, changing them is kind of annoying. The larger machines use a D1-4 mount, turn 3 cams with the chuck key, swap, tighten. You don't need to swap them out a ton, but there are lots of things you really need the 4 jaw for, and you don't want to just leave it there, as indicating every part in would get old fast. It is one way to get practice at it though...
All my insert holders are the cheap import, other than a couple really nice carbide boring bars. Most of the time, I use HSS, but sometimes inserts are the right tool, and the imports work well most of the time. I certainly wouldn't tell someone just learning to use $10/ea brand name inserts.
Hope that helps. Do some searching on this site. You will find a lot of old threads with info about various tooling, vendors that are trustworthy, etc.. One thing to search out is "leveling", alignment really. 2 collar test is one of them.
