Should I invest in a employer retirement and through my own broker or just pick one?

In general, if your employer offers a 401k or other tax-free retirement program, take advantage of it - especially if the employer offers matching funds.

For a more detailed answer that fits your specific situation, you'll have to sit down with some sort of financial planner who can take your age, your income, and your retirement goals into consideration.

In the US, annual contribution limits for 401k, 403b, etc. are separate from annual IRA contribution limit. So depending upon what investment options you have in your 401k or similar, you should put at least enough in that to get any company match (free money). But if you are "eligible" for a retirement plan at work (whether participating or not) some or all IRA contributions may not be deductible.

So if you do a split, you may want to go 401k and Roth IRA, since Roth IRA contributions are not tax deductible anyway (just tax free when properly distributed). A Roth IRA also makes a good emergency fund because you can withdraw the already taxed contributions any time without penalty (just not the gains). So that can grow tax free until or unless you need the money.

Invest in the employer's 401K and make sure to contribute enough to get all the matching funds offered. I assume you mean that your employer has an option for you to open a broker's account in your 401K or select funds offered by the 401K administrator. Unless you know something about buying stocks and intend to make stock selections yourself, I would advise using the various funds offered by the administrator and not opening a brokers account. The funds will be managed by professionals.

Yeah, the employer's plan would give you more if they match it. PoohBearPenguin is right. lol