Well
@Golem Pens, there almost no end to what you may want to get for working with the lathe to make projects, and we have lots of suggestions.
Maybe start with one or 2 measuring tools, as the lathe dials are in imperial, it maybe easier to figure depth of cut with imperial reading measuring tools or at least” bilingual”measuring equipment. AND get as big a wall chart of conversions that you can find and fit on a wall handy to the lathe. A good one will have drill sizes for tapping holes too.
A grinder of some type, capable of grinding tool bits, and a basic stone for touch up work to the bits.
I am sure you had some tools for making pens as you have already been doing it. Some, many, all, maybe still of use with the lathe.
A drill chuck, sized to take the drill bits you have already been using, allowing for some oversized for the future. Some center drills that will work in the chuck.
Thread gages, to start with, metric? if that is what you presently use in tap sizes.
How deep down the rabbit hole you go with tooling, directly corresponds to the depth of your pockets. The hard part is getting the tools you need to do the jobs, without the what ifs, one of them would be great thing, getting in the way.
All the suggestions are great, just depends on where you are going, and when.
And adding many of the suggestions is sometimes half the fun!