We read that you shouldn't use pull ups, as it makes training confusing and they think they've got a nappy on. We just carried potty in a carrier bag and lots of spare clothes. Our dc wouldn't even go near a toilet, so had to carry the bloody potty! It was only a few weeks though, then it all fell into place. About to start with dc2 .
I did use pull ups as ds started training at 20 months. It didn't confuse him and he was day trained by age 2. I never carried a potty about with me either but knew where to find a toilet wherever we went!
We have always used trainer pants, terry pants with a plastic outer. They feel wet to a child, need to be changed quite quickly but do contain a limited amount of wee and, we found, thankfully, as much poo as necessary! They did not seem to confuse training and we always referred to them as pants and nothing else and treated them as a promotion from nappies and to be kept dry/clean if possible. It was only our 2nd and later children who realised that they were in any way different from other pants and we simply said that other types of pants were for later when they were a little bit older. We bought from a number of different places but they seem to be much of a muchness - a fairly basic design which does its job.