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A traditional IRA is tax free going in, but taxed coming out. A Roth is the opposite and taxed going in, but tax free coming out.
Mathematically, they're equivalent. The only reason to choose one over the other is your personal income tax rate. If you think you'll pay a lower tax rate in retirement (because you won't be making as much, and thus will be in a lower tax bracket), then you'd pick a standard IRA. If you have a shit job now and expect to make more later, a Roth would make more sense.
You're correct about the now vs. later part but I'll also note that tax laws can change and some people think that getting ahead of the curve and confirming their taxes now via Roth has value. I'm not one of them, but it's certainly a strategy.
The only reason to use a Traditional IRA and not a normal brokerage account is so you can backdoor it into a Roth IRA. Since you can't make Roth IRA contributions when you are above a certain income limit, but you can roll over a Traditional IRA into a Roth IRA, this let's you avoid taxes on the growth of the account.
This is the real answer to the question given the nuance in the question of “if you make a lot”
As I understand it, the interest income is tax deferred while it is still in the IRA. So over a long period it can appreciate a lot more than if taxes were being taken out every year.
My understanding of this (just worked through it with my wife) is that you will not take a tax hit on the disbursement when you take it but you will get hit with capitol gains taxes on it's growth from inception of your contributions.
When you take it out, it has already been taxed but it will still count as income for your tax planning purposes in the year you receive it - hopefully you're in a lower tax bracket when this occurs. It is not a taxable income (though it counts as an income and increases your tax bracket accordingly) but it's growth since contribution will cost you at your current tax bracket as you take it.
Not a financial wizard here, ask a professional.
That depends on a number of details that may or may not apply to you.
You can contribute up to $6,500 ($7000 next year) to any mix of IRA that you're eligible for. There's a phase out range for deductions if you have a retirement plan at work (between $116,000 and $136,000 this year's MAGI, which is gross - payroll deductions). If you're married, your spouse follows different rules depending on whether they have a workplace retirement account.
If you're above the phaseout range, you won't be double taxed, but any growth will be taxed. So if you invest $6k and it increases by $3k, and then your withdraw it all at regular retirement age, you'll pay taxes on $3k. This gets complicated when you factor in the pro rata rule (e.g. if you withdraw half, you'll take half from each bucket, so $1500 will be taxed and $3k won't), to the point where I recommend people don't bother. The benefit is that you avoid capital gains on growth and only pay when you withdraw, which means any trades in your IRA aren't reported to the IRS.
If you'll likely be above the deduction range for most of your career, I recommend doing a backdoor Roth, which means immediately converting contributions to a traditional IRA to a Roth IRA, so you essentially get the benefits of a Roth IRA, but without being eligible. There are caveats here as well, so read up on it.
I'm happy to work through examples, I just need to know what your situation is.