Black Diamond Mini Pearabiner is what Tethrd sells for around $15, and can be found elsewhere for $10-15 as well. Great lightweight carabiner. Black Diamond Positron is a smaller carabiner, around $10 each and very similar to Pearabiner. I believe the new Trophyline saddle has these on their lineman’s belts, and the Pearabiner as their tether biner.
Metolius Bravo is cheap and strong. Can be found for $10 and under most places. Has my least favorite screwgate but it’s still a popular choice for good reason.
Fusion Essence is the one AeroHunter uses, and it’s awesome. Comparable to the Mini Pearabiner in price, the big advantage is that it’s auto-locking. I don’t know if I’ll put one on my tether yet, but I like it for my bridge and LB.
All 4 of the carabiners above are within a couple kN of each other in strength, and a couple mm of each other in size.
These are just the 4 I have personally used. I have also used lesser biners from Hunter Safety System (meh) and Muddy (double meh). The good stuff isn’t really more expensive than a 2-pack of HSS crapabiners, so get the good stuff.
There are LOTS of other good biners from Petzl and Mad Rock and Wild Country, etc. Go to REI if you have one close by and play with the gates on their biner rack. Also make sure the “basket” is slick enough to let rope/webbing slide easily for your bridge.
Good luck!