It is always recommended to meet in a publicly visible place.
For house siting, walks, and drop in visits, I’d suggest you consider meeting along the route where they normally take their walks (it may be a sidewalk, grassy area within their community). Ask them to bring the dog to meet& greet during a short walk when they’d be holding leash, during which you’d ask each other questions. Then, if following your instinct, you determine it’s safe, you can then enter their home and go over where everything is you’d access for dog.
For boarding, I’d suggest you consider meeting near your home near where you’d walk the dog (sidewalk, grassy area, etc.) and again while they hold the leash, start the meet and greet outside with asking each other questions.
Some sitters like you have asked to meet at a park or elsewhere, but that may mean 2 meet&greets have to be done for each potential client. It’s a lot of time and expense if you can figure out how to do with 1 instead. Unless the humans were super squirrelly (which I haven’t encountered), I place far more focus on the dog’s potential match. Meeting the owners without the dog is useless to me and not any different than a pre-screening call done over messages, a phone conversation, or internet based introduction (all prior to / not a substitute for m&g) which I can do from wherever I am located.