Choosing The Correct Size
While most individuals choose their rivets based on cap size, the best way to select an appropriate sized rivet is by its' post/stem height. This helps you obtain the most secure fit. The correct post height is when the post is peeking out approximately 2mm-2.5mm beyond the fabric. (2mm is less than 1/10" of an inch). Below is a helpful chart that provides a listing of rivets by popular brand along with the corresponding post height(s) offered. For riveting most handbag straps and connectors, a 9mm Cap size is quite common. But you may only need to use an 8mm rivet to secure the layers, especially if you want a lower profile look. This is because the post height for an 8mm rivet from some sellers, is the same height as a 9mm rivet from another. So it can also be an aesthetic decision. If you were using quilting cotton instead of thicker vinyls, a 7-8mm rivet may set more securely than an 8-9mm depending on the needed post height. The chart (below) will assist you in selecting the appropriate size rivet for your needs. (Note that the chart does not indicate available colors from each seller, and you may want to consider that as well.)
I will admit that I do have some personal favorites. However, I stock my studio with rivets from different sellers in different sizes and in different colors, so I can choose what is best suited for my project. If I am looking for a rivet that will be used more decoratively, I reach for the prettiest color. If I am looking for a rivet to secure a strap and don't want any issues, then I may compromise in color and go with the best durability. If I am choosing a rivet to use with leather, then I reach for my higher-end inventory. If I want to use the smallest cap-size possible (like for my little charm bag pattern), I will choose the one that has the longest post in the smallest cap size. If you only want to stock one-size rivet, you will want to consider the brand/seller that has the right post size in the color(s) you use most frequently.
Materials and Durability
Not all rivets are created equal. Some rivets are more durable depending on their material and how they are made. Some "softer" rivet materials are more prone to denting. Typically Rivets geared to the demands of leather-crafting are made with better materials and have taller posts, thus might be slightly more expensive. But the best rivet is the one that's sufficient for the job in the correct post height. For lighter craft projects you may not need to pay for a premium alloy. Conversely if you are using thicker and denser leathers, you can't afford to choose a less durable rivet.
Tools To Set Your Rivets
While you can use universal rivet setters (and non-branded dies on your press machine, if they fit), for the most secure set and compatible appearance (meaning no indents on the rivet or impression marks left on fabric around the rivet), use the compatible setting tools provided by or recommended by the rivet brand. The curvature shape of the cap's dome, post height, post width, and base diameter can vary for the same cap-diameter rivet. When it comes to setting a rivet, you can use a larger die to set a smaller rivet (e.g. using a 10mm die for a 9mm rivet). However, you run the risk of imprinting a circular dent in your fabric around the rivet cap. When you are choosing a hand press to install more than just rivets, such as for grommets or speciality studs, it is especially important to make sure your hardware is compatible with your setting tools as grommets and some studs can vary greatly.
Choosing a Hand Press Machine To Set Rivets
I currently have three "Rivet" Table Press Machines. Two are from Kam (the DK93 table press from KamPress.com) and one is by BuckleGuy.com. I am quite happy with all of these presses. The Kam Press is really a great value press machine for average use. And I highly recommend it to the average maker. The Buckle Guy press operates more smoothly and requires less effort to press, but is much more expensive. Both the Kam and Buckle Guy press have an approximate 19mm bottom anvil hole, and a M8 top rod screw, which is a universal size so there are many die sets that will work with the Kam. I use rivets from different brands on these press machines with appropriate die sets.
If you happen to be in the market for a rivet press machine, I recommend viewing both of these excellent videos on YouTube before your purchase.
Punching Holes For Your Rivets
This is my personal opinion -- It is a waste of money to buy a "hole-cutting/punch die" for a rivet/hand press machine. A single circular hand punch (with a mallet) is MUCH less expensive and does the job more precisely and with greater visibility for centering your hole. I prefer the individual circular punch drives for the cleanest and most accurate hole and because you have the greatest visibility into what you're doing.
You can buy an inexpensive #1 (2.3mm) circular punch tool by Tandy ($6-7), and it will work quite well. Or you may also consider a changeable-tip set such as the Osborne full Mini-screw-on set (below) or even a hand-Rotary Punch. For the two size holes i punch the most, and when using leather, I have very high-end circular punches by K.S.Blade. To me these were worth the premium. But for the average cotton, cork or vinyl bag maker, this premium would be over kill. Buy the best you can afford.
Osbourne Multi-Tip Set
Tandy Pro or Osborne Hand Rotary Punch