First off, I am so sorry for your loss. If you need to, please do take several months to deal with the death and aftermath before doing anything major with the accounts.
The only timely thing right now is to make sure to get the accounts labeled correctly as inherited (IRA/401K) and make sure that the required minimum distributions (RMD) for your dad were taken in the year of his death (this year?) before the end of the year. You'll also need to make sure your inherited accounts have your own RMD set up and ready to go next year, but you do have a bit of time for this. Make sure to ask the financial institutions that hold the accounts about this, as otherwise you could be forced to take the entire 2 million out over a 5 year period, which would suck because taxes are owed on all withdrawals.
https://www.fidelity.com/building-savings/learn-about-iras/inherited-ira-rmd^RMD rules for inherited IRA/401k based off of Fidelity's info
I started out pretty much the same: inherited a large amount from my father's passing. Pretty smart with money, saving at a great rate, frugal and investing (blindly) in my own workplace accounts, but not really understanding how the market and investing in general worked and it was scary realizing what I had suddenly and what I might could do with it if only I wasn't so dumb about the investing/market stuff. But I figured it was too complicated and would always need professional help and I was pretty fearful about "risking" my dad's gift in the markets. I took about 6 months to deal with the loss of my dad, did a whole lot of reading, and likely pestered the crap out of many folks on this forum (and others, but mostly here) until things clicked for me. All those links below are the baby steps I needed to figure it out.
Couple of things:
Who do you have your accounts with? Vanguard, Fidelity and T Rowe are all decent companies with great funds available, and there are a few others I've heard of that aren't terrible. There are some companies that ARE terrible tho, and make a point to have high fees and awful funds for investing, so if you care to share, we can help figure out if you're in a good place as far as that is concerned.
FDIC insurance is only for a bank failure/malfeasance, not investment accounts. Investment firms offer coverage for failure/malfeasance through SIPC (SECURITIES INVESTOR PROTECTION CORPORATION). Depending on who the investment account(s) are with, you are already covered in the very, very unlikely event that the institution will fail, or someone working there plunders your accounts and the company itself won't make you whole for their error.
With 2 million invested, you have a safe withdrawal rate of ~$80K if you leave the accounts invested in broad market funds (like index funds). Putting it all in "safe" things like CDs means that safe withdrawal rate isn't valid as you'll have very slow, if not stagnant growth, and likely spend down that 2 million over the next 20 years if not sooner.
Also to consider: required minimum distributions (RMDs) are going to be a thing if your dad's accounts were tax deferred (so like a 401k or a traditional/rollover IRA). As you are in your 60s, this means the amount on 2 million you're going to have to take out will be a bit higher than if you were in your 30s or if the account was only 100K or less... they will base the amount of RMD off of your life expectancy (as long as you get the inherited accounts set up correctly). So based off of your age/accounts, you will be taking out a rather high amount each year that will be taxable, and depending on other taxable factors, you definitely need to figure in taxes to be paid... this is not a terrible thing, but just be aware if you haven't been in a high tax bracket, you may end up in one going forward because of the RMDs. What I did was have the investment company set up an automatic RMD schedule and include federal tax withheld at about a 25% rate for the first year until I got things figured out, and then I dropped the tax withholding down to cover what I actually needed to pay.
It sounds like you are not very knowledgeable about investing in general, so I'm going to recommend you some reading to get things figured out. If you're not planning on retiring for another year, then use this year to research investing, figure out your plans and set up the accounts to work for you and support your future. Fear is a terrible thing to use as a planning tool, so to eliminate that, you need to do some homework.
http://jlcollinsnh.com/stock-series/^online or get his book. This series really made all this stuff easy to understand in simple language. This is how I figured out how this stuff works and I am not scared in the least about investing or market drops or what.
All of my recommendations (and most of the others on here) are going to revolve around index investing, basic Bogleheads stuff, based off of John Bogle's amazing fund structures. He wanted investing to make sense, be simple, and allow anyone to be successful - which is why tracking the entire market through index funds is so perfect for just about any investor. You don't have to be an investing wizard to do well at this - you buy index funds in the asset allocation you decide fits your needs (there are stocks and bonds and even real estate index funds out there). And then you leave them alone, only checking once a year if you'd like, to track the market.
https://www.bogleheads.org/wiki/Investment_policy_statementhttps://www.bogleheads.org/wiki/Asset_allocationhttps://www.bogleheads.org/wiki/Main_Pagehttps://www.bogleheads.org/wiki/Getting_startedAnd ask LOTS of questions on forums like this one. There are some great people that are smart and don't mind helping out.