Another vote for an ER32 collet chuck and collet set. The collets will come in useful when you decide to buy a milling machine!
Don't expect much from milling in a lathe. The work envelope is tiny and lathes lack rigidity because they're designed to resist turning forces, not multi-directional milling forces. In consequence lathe operators can only take light milling cuts and have to organise lots of ingenious work-holding.
Lathe milling was once very common, but I found it immensely frustrating. I agree impatience is one of my defects! However, jobs that are an absolute doddle on a real milling machine become challenging projects on a lathe, especially small ones.
If it doesn't go well at first, reduce expectations and practice, practice, practice! I found milling on a lathe needs more skill than most other lathe work.
Dave
Edited By SillyOldDuffer on 04/04/2023 16:04:50