Avoid cheap ring holders with permanent adhesive or those sketchy ones from dollar stores - they genuinely bond to your case and rip off pieces when you remove them. Also skip anything that uses a super strong contact cement unless you plan to never change cases. The adhesive quality matters way more than the brand name, honestly.
PopSockets and Spigen both make versions with removable adhesive that's designed specifically for this. Their pads use a gel-like adhesive that sticks firmly but releases cleanly without leaving residue. MagSafe-compatible rings are another route if your phone supports them - no adhesive at all, just magnetic attachment, so you can swap cases without any worry. If you're switching cases frequently, MagSafe is probably your best bet since there's zero adhesive involved.
When you do use adhesive rings, clean the case surface really well first with a dry cloth to get rid of dust and oils. That helps the adhesive work better and release more cleanly later. If you need to remove one and it's stuck, warm it gently with your hands or a hair dryer on low heat for a few seconds - the adhesive becomes more flexible and peels off without tearing. Test any new ring on an old case first if you're nervous about it.