Shit man, I guess first dates are never comfortable.

I can't help you in your question but I will give you some feedback on experience with first dates that lead to sex!

I meet some chick on a night out, exchange numbers, text for a bit then meet them for a first date.

The first date usually ends up with me and the girl totally wasted at Wetherspoons (classy). Afterwards we go back to mine and do the deed (fuck).

Trouble is after that night, the girl usually feel like she's disgraced herself by putting out after a few hours and I will a) turn into a booty call b) never see the girl again.

To summarise, unless your primary goal is just get a lay, don't worry too much about sleeping with her after x amount of dates (5's the limit) but emotionally get her attached to you.

Sex isn't the answer if you're looking for a relationship.