I agree about the card, think it would be better to send your own card, and let others make their own efforts. But having moved a great deal here and abroad, I think it would be appreciated if you got a little collection of information together and offered it to them.
So .whenever I moved , I would always go to the library, because not only can you enrol , and make use of all the things on offer there, but they usually have the up to date address and phone and email of all the clubs and societies in the area, So if they already have some interest such as gardening or whatever, it will give them good introduction to what is available there. Also the libraries often have up to date notices for things going on. If you have a useful bus route to a local shopping centre, you could give them a bus timetable, and if you have a local paper, you could get them a copy, as again it will have a whole load of information from what is happening, and often has reports on clubs and what is generally going on locally. Another thing you might do is tell them the way to places like local butcher, baker or whatever, and where the doctors surgery is.
We all have our own preferences, but for the first couple of weeks it is very helpful to have a recommendation, for trustworthy places, such as good garage or handy man etc.
I am not suggesting you should do it all at once , but this kind of thing is much appreciated and also perhaps any cafes or pubs that you might know are good, as whenever you are moving there is so much to do, that you get exhausted and to be able to get fish and chips or a pub sunday lunch nearby, is worth knowing about.
Actually as I was used to moving a lot, when selling my own houses, I used to have a little notebook, and write in it all this sort of information, plus contacts for any plumbers, central heating installers, that we had used. plus I used to do a little plan of the garden showing where things were growing etc. It was always gratefully received for that first bit when you dont know where anyone or anything is. This probably sounds too much all at once, but I am just flagging up some of the possibilities that you might like to consider.
It is very nice to be a welcoming new neighbour and I hope all goes well for them and you.