Welcome to the forums Bran.
You ask all the questions that a usual first time poster would. It's good to see that you're looking to improve, though. The first thing I see in your post that you might want to change is the following statement : "I'm ready to date".
Don't take offense to anything I say, as you'll find I'm one of those blunt types on the forums. I'll tell you like it is, whether you believe it or not. You just got out of a LTR? I doubt you're ready "to date". Your mind might be telling you this because you're so used to being in a relationship, but it's not healthy. This is what I call jumping from one unhealthy relationship into another. It NEVER works.
You shouldn't be thinking you're ready to date another girl. You're much better off doing what a lot of us call "spinning plates" aka talking to plenty of women. Get back into the single life, have some fun, and don't limit yourself. You'll find that when you're single, you'll really find out who you are inside and make your BIGGEST improvements. Instead of concentrating on approaches or lines, work to improve yourself. What you say to a woman is the LEAST of your worries. It's HOW you say it and what confidence you have when you say it to her. We always say women have a sixth sense when it comes to men. You can say the right things, but if she senses that YOU'RE not confident about yourself, she will flake.
What's my mindset when I approach? If anything, it's SIMPLE. The last thing you want to do is over think. A simple smile and Hi my name is ____ will always work if you say it with confidence. As for continuing conversation, well that's something you'll have to learn through trial and error on your own.
Again to recap- have fun being single for awhile, make some new friends, improve yourself physically and mentally, and don't "look" for a new relationship. Things will come when they are meant to come. Usually you find things when you're NOT looking for them. You'd be surprised. best of luck in the future
