I usually suggest something like a walk in a park . Less distraction, and no money need be spent. I figure, if we can't get along doing something simple - anything else is a waste of time.
No formula to this really. I'm myself , regardless of who I'm with. I treat people kindly, with respect, and insert humor early on, so I can gauge their ability to have fun. Even when I've met someone that I suspect will be a one time meeting - for whatever reason, I try to have good conversation, with both of us leaving with a smile.

Either we click, or we don't !

Like a possible best friend!!

It completely depends on what I know and how much interaction we've had ahead of time. Personally, I will not put on a big show and be genuinely who I am. I am looking for a partner, not some dope I tricked into things

I don't do many fancy dinners, so assuming we've talked for a while and have shown some compatibility, I will pick a fancier place and simply state up front that I am paying for dinner. There is no reason to play games about finances or to try and impress someone, but a nice Italian dinner with wine is something I enjoy and cannot find it in me to enjoy alone. I can enjoy steak alone, but if I've had a hankering for steak I'll make a similar proposal. However, I am showing up in a Honda Fit and being a practical person and if we end up going for drinks afterwards or something, split bill is fine by me. Jeans and a collared shirt, no sneakers.

If it is a rando off a dating site that I've only chatted with briefly, but wants to meet to weed out the psychos, it'll be much more casual and have more escape routes. An artisanal pizza place or a coffee shop is great. No shorts, somewhere that's good for conversation. Never, ever a place I normally go to. Whether the girl reaches for her purse/wallet is a serious factor, even though I generally intend to pay.

I'd expect respect, first and foremost. Respect of my body, my temperament, and my beliefs. The non-religious ones, I mean. The small degree of spirituality I have is not really important to me. Aside from respect, I'd expect them to try to give me a memorable or pleasant experience, preferably in the form of a cool, romantic date.