Definitely agree with the keeping time to yourself advice, although I wouldn't subscribe to specific set limits, definitely don't let your own hobbies/friends/me time drop for any fledgling relationship.
Emotionally investing would be, your mood, or more worryingly your self esteem, being significantly affected by whether a date went well/whether he called/texted or not, spending time over analysing dates or messages, picturing too far ahead in the future etc.
Enjoy things in the moment for just what they are right now, not what they could possibly be in the future.
Be aware of your boundaries and what counts as red/yellow flags for you. If someone doesnt respect your boundaries or waves a yellow flag, don't be afraid to use clear, open honest (non-confrontational, non-accusatory) communication to get across what the issue is that you've noted and it's not ok with you for X reason. Decent people who are into you respond to that with an apology and will then respect boundary/alter behaviour. If they don't then there's a fundamental lack of comparability anyway.
If you spot a red flag don't second guess yourself or try to justify it. It's their loss. Bye bye. You don't need a fixer-upper.
If you're venturing out into the modern dating scene, educate yourself about "seduction philosophies" like The Game, Pick Up Artists etc so you can spot and immediately discount idiots who subscribe to them and see women as an inferior class to be caught and controlled for their own purposes. Don't engage with them, just delete/block and feel sorry for the sad delusional sods.
On the more positive side of things, remain open to new ideas/experiences and give anything a try once; be yourself, and have fun. Try not to be constrained by a narrow view of who you're looking for or what you're expecting.
A HIMYM rule that I stick to is not planning further ahead than the length of time you've been together. It's just unnecessary pressure.