Roth IRAs.. Is it better to invest with the larger companies/funds?

[Jimellow]

Is it a good idea to invest/start a Roth IRA with one of the larger brokerages, such as T. Rowe Price, Fidelity, Vanguard, etc., that have many different mutual funds that will allow me to move the money around throughout the course of my/its lifetime?

For non-IRA investing, I will deal with a smaller and less diverse brokerage, that may only offer 3 mutual funds, however, when it comes to an IRA, it seems the diversity of a larger brokerage might be nice, due to the money being "stuck" there for many years.

As an aside, that is also relevant here... Is it true that if I would start a Roth IRA with Fidelity (for instance), I am able to later switch that money over to a fund with T. Rowe Price? I believe I was told there was a 60 day window that allowed such cross-brokerage transfers to be made, but I would appreciate some clarification as to whether that is possible or not. That too would be important in regards to whether I opt for a smaller or larger brokerage to invest my IRA money into.

If no such transfer is possible, then it would seem very important to start off with a larger, and more diverse, brokerage, whereas if transfers across brokerages are possible, the initial selection may not matter as much, as the IRA could always be transferred elsewhere later, if I want to try a different fund, etc.

Thanks!