I work in the financial institution related industry and we are required to take specific "compliance" courses every year. Several of these courses deal with laundering money and such topics as that.
One thing I learned from all these courses over the years is "big brother" is really watching every penny and has a tracking and a reporting process that the common person (you and I) will never, ever see or know about.
In the end, if financial transactions are above the board and the money can be tracked via a paper trail, there really is never a problem, even large sums of money transactions. If transferring from one financial institution to another financial institution (for example 401K retirement accounts, IRA's, even Health Savings Accounts), those transactions are conducted between institution-to-institution, even across states, and even if you are using different addresses on the accounts. People move, people get different jobs, people are in a constant state of motion, more so today than ever before.
The thing "they" are looking for and truly are concerned about and gets "Big Brother" all upset are cash deposits and cash withdraws over specific limits, and those limits are accumulative. Cash is not so easily tracked. And that's where the real red flags are raised.
Starting or opening a new financial account is no problem at all. You will be asked a battery of questions (by law they have to have this information). You will probably do an interview, be it over the phone or in person, and you won't even realize the information they are collecting on you, because the conversation will be so informal. But what they are fishing for is to determine if you are legit or truly a criminal element. If you are above the board, you'll have absolutely no problem, and red flags will never be raised. They still do their reporting, and then things settle down.
Right now, even your current accounts are being tracked and monitored. If you were to make several deposits into once account today over a specified amount, and especially if it were cash, then you'd be red-flagged.
But really, I don't know what happens after that if you are "suspect" of criminal activity.
As long as you are truly accounting for your funds, have a solid financial trail where the money is coming and going to, you'll have absolutely no problems.
And .. you may consider Merrill Lynch also in addition to Fidelity. Seems the last 20 years of my life, the companies I've worked for like to flip-flop back and forth between these two. Both are good.
Good luck.