Head over heart is the biggie. Don't get sucked in to the love/romance side of things without giving equal thought to the practicalities and realities. It's too easy to start ignoring the red flags when you're "in luuuuve!"
Equality. Keep things equal right from the start. Me and OH had a "joint purse" when we went for day trips or holidays together at first. We'd both put the same amount of money into the purse and then use it for "equal" spendings like a meal if we both ate/drank similar priced items, or bought similar priced souvenirs, or attraction entry fees, etc. If one of us wanted something that the other didn't, then they'd pay out of their own money. Neither of us ever felt beholden to the other nor that we owed the other anything. Put us on an equal footing virtually from day one which worked well as we bought a house together, got married, had a child, etc. We've always been equal financially - it's a good habit to get into.
Self respect. Never do anything you don't want to do or aren't comfortable doing. Don't let the other person start playing the emotional blackmail card. Learn to say no, and mean it.
Boundaries. Set your boundaries early and stick to them. If you want to go out with the girls every Friday, then continue doing it, whether or not your new partner likes it or not. If you don't want to sit like a lemon watching them do their "hobby/interest" every Sunday, then don't go. Ever.
Red flags. Take notice of any red flags. Don't let them persuade you it was someone else's fault, your fault, "because they were drunk" or any other feeble excuse. If they do something or act in a way you don't like and aren't comfortable with, read the signs, and walk away. Learn to realise you're not going to change them and don't waste your time trying.
Far better to find out what your prospective new partner is really like as soon as possible so you can make an informed decision whether there's a future or not, and best to walk away early.