For many years I was exclusively a Schwab customer.
Then I got 15,000 miles for opening a Fidelity account, plus I like the Fidelity Spartan International fund. Then I took advantage of TD Ameritrades miles+ money offer. Recently, I moved my Vanguard GNMA fund to Vanguard so I could convert to to admiral shares.
So now I have 4 brokerage accounts, but I'll close Ameritrade soon.
IMO if you are almost exclusively a mutual fund person Vanguard is the way to go. The funds have lower expense and the fact that fund holders profit from most of the fees, means that generally Vanguard is lower cost than any one else.
I think if you are primarily a stock investor Schwab is superior, although the difference between Fidelity and Schwab are pretty close. Fidelity has slightly cheaper commission $8 vs $10 (for large accounts), and the Fidelity One view is terrific. On the other hand Schwab has superior research information, and offers a wider range of investment opportunities (IPO, alternative investments, etc.) and has a terrific active trading platform Schwab StreetSmart Pro. I think it is a toss-up between Fido and Schwab as to who has the best website, with Vanguard a distance third.
If your IRA will be a mix of funds, stocks and ETFs than Fidelity may very well be the right choice for you.
One strong bit of advice try to consolidate financial activiities with one of the big 3, at least until you get to the $250K and later the $1 million. Once you get to a million in household assets, all of them add numerous free services, and eliminate tons of fees (wire transfer, overdraft, checking etc.) I recently had to open a bank account for the first time in more than a decade, and I was stunned by the myriad of fees that banks charge for services that Schwab gives me for free.