You have given your lathe size, but not the method of attaching your chuck or what size spindle bore.
The most common collets seem to be the 5C and ER type. I have a similar sized lathe and what I have figured out is 5C are really intended for a bigger lathe.
There are chucks that will allow you to use them on a smaller lathe, but they need a larger than 1" spindle bore to use a draw bar so you are losing some of their effectiveness on a smaller lathe. Often the chucks used for a smaller lathe mount in the spindle bore greatly limiting your ability to run material into the head.
There are 3C collets which use the same design as 5C but are designed for smaller lathes with a 1" spindle bore. They are less common so more expensive (also smaller capacity than the 5C).
The major downside to the 5C and 3C type collets are their very small range, so you need to have a lot of them. A comprehensive set will have 1/64" steps so around 70 collets (for 5C, 3C being smaller would have less).
ER collets seem to me to be superior for small lathes since they are designed to work off the front of the chuck so they are not limited by the spindle bore regardless of size. I have an ER32 chuck on my Sherline which has spindle bore a hair larger than 3/8".
ER sizing is based on the nominal size of the outside diameter of the collet in mm (an ER32 collet is 32mm or 1-9/32" in diameter). They can hold work to about 70% of their stated diameter (ER32 1 9/32" outside diameter, and 7/8" is the largest size work holding available for the size).
The other advantage is they have a much larger range of work holding, it varies by size with larger collets having a larger range, but sets are generally stepped with 1/32" at the smaller end to 1/16" increments on the larger sizes. So a comprehensive ER set only needs 1/3 to 1/2 as many collets as a 5C set. This range also means you really don't need to have both metric and SAE sizes.
Since ER collets come in a wide variety of sizes (ER11 to ER50) you have the option of buying multiple chucks sized to your work (small chuck and collets for small work, larger chuck and collets for larger work) or just buying one chuck sized to your largest work and getting wide range of collets for it based on what works best for you.
There are many other collet types but these two seem to be the most popular for hobby users.
3C/5C used to have an advantage of offering other shapes than round, having square, and hex shapes available, but you are starting to see these offered for ER collets as well.