I would like to keep in touch, get to know the person, develop a relationship,,, give them a call once in a while and find out how they are doing etc. and tell them how I'm doing... you know, general chit chat...and yes if I'm looking for a job, I'd eventually bring it up in one of my casual chit chats and ofcourse if the person is in a position where he can be of help, they will most likely notice that and keep it in mind for when an opportunity arises... I would not hire anyone because he is a friend or a friend of a friend unless I know they are capable of doing a good job.
Your approach is exactly what I would expect from others and something I would also adopt if I was ever in such a situation. Subtlety goes a long way in expressing professionalism… and I’m not saying this because I don’t want to help. To give you an example, I’ve personally helped out a couple of other guppies over the years through recommending them directly for certain jobs but I did this because I had met them a few times… and I knew that they were looking for work – but they never insisted or kept bothering me to set them up in my workplace.