A collet chuck by definition should normally attach to the spindle nose in the same manner as any other chuck. Probably 90% of the many that I've seen handle 5C collets. Most of the remainder handle ER-nn European type collets.
The other general type of collet, usually called a draw-in collet, mostly uses a draw-tube and has an adapter that mounts in the spindle's taper. The draw tube can have a hand wheel for tightening or a lever mechanism mounted to the left end of the spindle.
This collet type is limited in maximum diameter to the ID of the draw tube (except for the MT types). For the 618, the collet part number is M6-751. According to the factory drawing, that is around 9/32" as the counter bore diameter behind the gripping area is 19/64". The almost sole exception to this diameter limit are (at least for the 618) 2MT collets, which usually use a 3/8"-16 draw bar and cannot pass work through the collet. 2MT collets are usually used for holding various sizes and types of milling cutters. AFAIK, they are only available in 1/16" increments and, because their gripping range is only about +/- 0.005", are not generally used for work holding as they can't handle in between sizes. When you can find sets, they usually cover the range 1/16" to 1/2" in 1/16" increments.
The Atlas M6-751 has been referred to in one or more eBay ads as type 6A. 6A is not on any of the collet lists I have (currently showing dimensions for over 79 types) but could be correct. However, as you have found, they are rare.
All things being equal, if you can only afford a set of one type, I think that I would recommend either ER25 or ER32. These are double ended collets that look like overgrown examples of the collets in a Dremel and other small grinders. There is currently on eBay a conventional back-plate mounted ER32 collet chuck and 7 collets of the sizes that you would need for holding milling cutters with standard diameter shanks for shank diameter from 1/8" to 3/4". A full set of ER32's would be 1/64" to 3/4" by 64ths, a total of 48 collets. The two disadvantages to the ER collets are that being quite short, they are a little less stable or accurate on the spindle axis on lathes and they are considerably slower to change a work piece in. Which could be important if you were making a lot of the same part.
