As noted, Brother has a lot of different styles of machines and types of tapes The model number of the machine is less important than the type of tape. For the OP's purpose, look for a machine that uses "Laminated" tapes. These tape cartridges use a thermal ink to transfer the lettering onto a clear or colored background tape, and then laminate a clear tape on top of it. My machine uses "TZ" tapes, and Ive found them to be very durable.
At the office, they have a machine that uses smaller (and cheaper) metallic look tapes that are not laminated - these are not nearly as durable and the lettering can wear off easily.
For the laminated tapes, about the only time I've ever had a problem with them is when using them as wire labels and wrapping them around a wire. Over time, the clear lamination tape tends to come loose and start unwinding. My solution is to print the label twice on a long piece of tape, and fold it over the wire to form a flag, sticking adhesive to adhesive. Since doing this, I've not had any de-laminate or come loose on me. I've not had any problems with the laminated tapes on flat surfaces, even exterior.
Adam and Sue, and a pack of little furballs
2007 Holiday Rambler Endeavor 40PDQ Limited Edition - Cummins ISL 400
2013 Ford F-150 FX4 toad - USGear Unified Tow Brake, Roadmaster Blackhawk II Tow bar, Blue Ox baseplate
Home base near Buffalo NY, often on the road to a dog show