I use mainly 5C, a few 3S collets, and of course J8 for the Bridgeport. The 5C's are the go to ones, mainly because they can be used on several tools and machines. They fit both my 10" and 13" lathes as well as the spin indexer, and end mill sharpening fixture. This system does require a good supply of collets. My set of round collets goes from 1/64" thru 1 1/16" by 1/64ths. I also have a hand full each of square, hex, step and splines. You can also purchase "emergency collets" that aren't hardened and can be bored to any shape or size. Most sizes under an inch will have internal threads which allows the use of a stop for making multiple pieces the same length.
The downside is like most good tooling they can be expensive. If you go top of the line Hardinge they're over $40.00 per copy. If you buy lesser quality like Shars they can cost as little as $7.00 per copy. I got lucky and bought a nearly complete set of Hardinge from a used equipment dealer for around $5.00 per copy. I filled in most of the missing ones with Shars "High Precision" collets for a little less than $10.00 per copy. The Hardinge have a holding range of +/- .007" to .008". The ones from Shars have a holding range of +.000" to - .015". Hardinge used to advertise a runout of .0002" or less. This information doesn't appear in their current advertising. The Shars standard collets are advertised as having a runout of less than .0006", while the precision line has a runout of less than .0005"
This style collet can be purchased in a number of different profiles like smooth or serrated round, smooth or serrated square, hex, rectangular, spline, and step. They are also available in different materials like brass, and nylon as well as special sizes or profiles, and in letter and number sizes as well as metrics. I'm not aware of any other style collet that can be purchased in as many styles and profiles as the 5C's. That being said If money is a concern I would start with a set by 1/16". When buying by the set the The Shars (15 pc) "Precision" collets are a little less than $8.50 per copy, while the "Standard" (18pc) set is slightly over $7.00 per copy, and includes a collet rack.
As an FYI I'm not hung up on the Shars brand. I do have a number of their collets, and have been satisfied with their quality. There are however a number of vendors offering similar quality collets. I mainly use Shars because they're from the area, and have always provided the quality they have advertised. They don't always have all quality levels or sizes in stock. Some sizes they don't carry. The last 2 I purchased came from All Industrial Supply, and Meitong Industrial supply because Shars didn't have those sizes at the time I needed them. They seem to be as good as the Shars "precision" ones, but slightly more expensive.