Besides my 401k should I fully invest in an IRA BEFORE I invest in mutual funds outside tax-advantage accounts

Simple answer: YES... and make it a ROTH.
If you still have money to move after that...THEN get into a reg brokerage account.
( NOTHING beats that TAX-FREE income after years and years ( and years) of gains... choose your funds well, and keep an eye on them... start out sort of aggressive and then down the road , move into balanced funds to protect that nest egg.)

if you have a 401k you can only add to a Roth IRA not an IRA, and only if your income is below a certain level. I recommend that you do invest in a Roth, especially if you are young. < 50. You should also have money in taxable accounts for any emergency(savings and investments). so after the 401k, try to fund both Roth and savings until you have 3-6 months of expenses. then go for the Roth to the limit

http://en.wikipedia.org/wiki/Roth_IRA

The answer really depends on your timeline. Remember that 401k and IRA money (Roth IRA included) are all for retirement, which means that you can't really touch the money until you are at least 59 1/2 without paying penalties. So for long term money, you'd want to max out your 401k to get the most matching contributions, and then contribute to a Roth if you can, or a regular IRA.

Aside from that, for medium term money (like savings for a home, or other major purchase) a non-qualified investment account is a good idea. The risk you'll want to take, and the amount of money in the stock market will depend on how soon you'll need the money. But an investment account will typically outpace inflation where a regular savings account or money market will earn only about what it takes to keep up with inflation.

So the answer is probably both, unless you're only saving for retirement.