First thing, good for you! :)
Second, you need to do lots of reading and get up to speed on the correct terminology and methods of basic investing and how the market (basically) works.
http://www.investopedia.com/ is a good source for basic definitions.
You sound a bit confused saying you'd like a mix of Roth IRA and index funds...
Things like 401k/403b, Roth IRA, traditional IRAs, taxable brokerages...
those are all types of accounts. Just like you'd have a savings account or checking account - they are holding buckets you put your investments into.
Index funds are a type of investment. They are a classification of a mutual fund or exchange traded fund (ETF), but not all mutual funds/ETFs are index funds. You can have an index fund inside of a 401k, or a Roth IRA, or whatever.
To get a basic understanding I'd suggest you read Jim Collins' stock series through:
http://jlcollinsnh.com/stock-series/It is long, but worth it.
And further good reading here:
https://www.bogleheads.org/wiki/Main_PageAnd you should be taking advantage of the tax deferred accounts as much as possible (things offered through work like 401k/403b or traditional IRAs in most cases) because they have the two fold benefit of reducing your taxable income now (meaning you're paying out less to the IRS each year) and investing it now so it's growing tax free as well. Super awesome!
You absolutely can tap traditional retirement accounts before 59.5, so do not avoid them:
http://forum.mrmoneymustache.com/investor-alley/how-to-withdraw-funds-from-your-ira-and-401k-without-penalty-before-age-59-5/It will be up to you to figure out whether it makes more sense to have traditional or Roth IRAs (it's based off of your income now vs. what it will be in retirement and whether you do end up creating a Roth pipeline).