I'm going to add the following disclaimer before I start.
Here are my top 10 things on what not to do or to do when starting/running your corp:I play only on permas, so these might not apply to running a corp on a rebang.
1. DO NOT put your password in your quote or shout it in game, this will only open you up to dishonest players who will rape you for what you are worth.
2. DO NOT spam "HIRING CORP MEMBER". A much better way to find corpmates is to work with a player as a contractor, and by talking to players. This will earn you that players respect and you can determine the trustworthyness of potential corpmates.
3. DO pick your battles wisely. This is a lesson i learned from Maagrath(Wicked Inc.) on P5. In short the big corps are big for a reason. You cannot achieve anything more than a aggravation factor for a large corp who not only has more resources, but probally a better method of attack than your new corp.
4. DO work with the top dog corps. Large corps (unless they are based on invading/combat or simply unreasonable) are usually more than willing to work with new players/corp as long as you agree to leave their corpmates and cols alone. They might even provide some support in the form of creds/lasers/protection while you get started.
5. Be open to diplomatic solutions. Most open wars can be avoided by simply taking a second to mail or /t a CEO or corpmate and working out a solution. Unless the player is a prick or unreasonable they want to be left alone...just like you do. An offer of a mutual NAP (Non aggression pact) or at the very least a cease fire will often be more than enough to resolve most problems. War should be avoided if at all possible, it only hurts both parties and slows down overall progress. Sure you might win the war, but now you are weakened against other corps may take advantage of you while you recoup from your war.
8. Take responsiblity for your corpmates, if they do something apologize for them and handle the problem internally. If you spend the bulk of your time fixing problems caused by a corpmate kick them. Even if they take a lot of cols with them, you will be better off in the long run. Especially if the corpmate is more aggressive than your corp model, this will probally keep you out of a war.
9. Pick your corpmates wisely, good corpmates will make or break your corp. Just don't hire someone because of exp or followers, get to know them first or ask vets on who they think will be a good fit for your corp. Once they know your play style...they will probally know of other players who would fit into your corp. Also, don't base the quality of a corpmate on their exp, my most valued corpmates were new when i hired them, interview and contract players to see them in action and see if they will fit into what you want from your corpmates. Also don't just take good fighters and invader, try to get a well rounded corp with builders and fighters/invaders.
10. DO keep corp communication open. This is your most powerful tool. You must communicate effectively to your corp so they know which direction you are heading and will stave off most diplomatic misunderstandings. Send mails daily to let corp know what is going on, who is ok to invade, who allies are, who NAPs are, etc. Communication will guaruntee your success or it will be your downfall.
I hope someone finds this useful.