Can I take my IRA money and invest it in mutual funds with a brokder and incur no penalties?

Yes. More or less. Depends somewhat on where your IRA money is now. If it is in a CD, you will suffer an early withdrawal penalty. If it is invested in stocks somewhere, you may suffer a loss upon selling them.

If it is sitting in cash somewhere, ask the mutual fund company to do a direct transfer. If you mean through a stock broker, then the stock broker may charge you a fee to invest it in a mutual fund. Some charge $75 to do so. It does depend on the mutual fund. Some mutual funds can not be purchased through a broker. Most brokers if the funds reside there currently will also charge you to trasfer the funds to the mutual fund company. They love charging fees.

As far as government penalties, there will be none so long as you do a direct transfer. Do not have the money pass through your hands. That is a no no.

If it's a Traditional IRA and you keep it that way...its just a simple "rollover" no problem.
If you want to convert to ROTH...you'll pay some tax...( really no need...just make your next IRA a ROTH if that's what you want)
Log on to Fidelity's web site and a rep can handle the rollover and put your money into an account where you can pick and choose... funds, stocks, whatever!! Good luck

Yes you can do a rollover.But don't go to a broker, Go to Vanguard they are good and will do it for you. Look at their Equity Income Fund it is a good one.