Sorry for the delay in responding - was out of town attending another funeral.
There are two generic collet types - solid and hollow. Common examples of the first would be MT3 or MT4 (or maybe, although I never saw one) MT4.5) and R8. These will only hold short workpieces and are more commonly used to hold cutters and drill bits. Examples of the second (that might be of interest for your machine) are 5C and various sizes of ER. Both are quite commonly available.
There are three basic types of collet closers. One is built similar to and attaches to the spindle like a chuck and may be described in ads and catalogs as a "collet chuck". The second is a drawbar (for solid collets) or draw tube (for hollow ones) that runs through the spindle with a handwheel on the left end and threads on the right end to fit the collet threads. The third also uses a draw tube but in place of the handwheel has a pivoted lever, hydraulic cylinder, or some other means of quickly pulling on the drawbar or draw tube.
Solid collets generally fit the spindle taper directly, although you could use an adaptor. Hollow ones could fit the spindle taper (there are a few spindles made that way for 5C) but more usually have a closer adaptor that fits the spindle taper and that the collet fits into.
Robert D.