I will ask where you are located, as, if you are outside the US, you may have different sourcing options, and in some places in the US, you may have local sources that are more economical than others.
As an introduction to ER collets, you might want to look at the Haas video “ER Collet Essentials” on youtube. (search “HAAS ER COLLET ESSENTIALS” on google or search engine of choice it will be near the top)
If you invest in the 3mm collet, be aware that ER collets (in ANY series) can not be used for larger than nominal, not even 0.01mm. Be careful to keep track of which is which. I don’t know that it is really needed. These collets run quite true within the entire closure range, hold well across the entire closure range, and 0.17mm (1/8" collet on 3mm) is well within the rating, but you might get slightly better results with the 3mm.
With a small thread mill, I would be more concerned about runout due clocking the tool and collet in the holder than due to collet size. If you have available, use a 0.0001" or 0.002mm test indicator on the tool shank just above the business end, and rotate the spindle to measure runout after snugging. If it is more than you want, loosen and resnug. Also try rotating the tool and collet in the spindle then resnug it. You will likely find small variations due to position, and small variations each time you snug in a given position. This is normal, and you just find acceptable runout and go with it.
When using the thread mill, you will need to compensate for the exact size. If you can test the threads with a go/nogo gage, that is best, but for many purposes, is not needed. Start by specifying the tool as LARGER than it really is in the CAM-- a few 0.01mm–, especially if you have only catalog tolerance (not the exact size), so the cut will leave a little extra material, then run a thread and check. Adjust the size of the tool smaller in small increments until you have it correct. It is common to sneak up on proper size, especially for critical dimensions and very small features. It is also common to tweak the tool size as needed to tune a fit or adjust for actual tool size variation (new, the tools from reputable suppliers used in these machines are usually pretty tight on tolerance, but it doesn’t hurt to check. Resharpened can vary a lot)