Obviously you will need Go sets. Most people believe 9x9 is the best size to start teaching on, and certainly the length of game played on 9x9 is the most suitable for the amount of time people will want to spend on their first game. If people come back for more then you could introduce 13x13, but it is not essential.
9x9 sets of stones in pots with secure lids is the best playing material to bring, but beware of being outside when plastic stones may blow away.
Beware of having a 19x19 board on the stand. Often someone who has played before will turn up and want to play on the big board against one of the teachers. This then has the affect of locking up half your teaching space and teaching resource for an hour or more. If the board is not there then the problem goes away. Especially nice though is to have a Go ban to look at, though usually this is impractical to bring because of the size and weight, and because it takes up a lot of display space. If you have a 19x19 mat then it would useful just to show the size to students, but keep it out of sight of the returning veteran.
Sometimes it is possible to have a seperate playing area - say in a lounge or cafe - and leave a suitable set for people to play on - though security may be an issue.