You only become a player when you're having sex with multiple people in a short space of time.
It's perfectly fine for you to meet and get to know multiple men in the same week, or even on the same day.
Think of it as it being like you going on several test drives for various cars at several dealers in the same week-end.
It's only if you put down the deposit on multiple cars that life becomes awkward.
Please go ahead and date both men. Date other men too, if you come across any you're attracted to.
Put Mr Ninety Minutes in the last chance saloon. If he's more than 30 minutes late for your next meeting drop him like a brick down a well.
As a good general guideline for any meeting, whether personal or for business: up to 20 minutes late without explanation is fine. Anyone can get held up by traffic etc and 20 minutes is no huge deal.
When you get to the 20 minute mark ping them "Where are you?" Give them 10 minutes to respond. If they don't; walk away and get on with your day. If they do respond make a decision as to whether to wait longer or not.
Give them the chance to reschedule any broken meetings.
Avoid the mindset of you going well out of your way in order to give a good first impression.
Argov's book Why Men Love *****es goes into detail on how and why you shouldn't be a doormat.
Men will be more attracted to you if you're assertive, respect yourself, value your time - especially if you're also positive, enthusiastic, light-hearted, good company in person.
It's better if you don't give away your home address until you know a guy well. Meet very close to your home, but not at your home.
And you know what your mum told you about getting into cars with strange men...