Where should I begin investing my inheritance?
The first step to investing is to know yourself and then to have a plan. Knowing yourself means knowing your current financial situation (Set aside money for emergencies and reconcile your cash flows) and your risk profile (Ability and willingness to take risk). Planning inolves making your life comfortable for the present and the future within your means. Once you have this in place invest for the long term to achieve your goals. Short term goals should be met with your earnings and funds in cash and other stable assets.
I recommend having 6-12 months of your expenses in highly liquid cash equivalents.
Assuming you have taken care of all that- the best strategy is to build a portfolio of stocks and bonds based on your risk profile. For eg: If you are relatively younger and have a good job, you can take on more risk for the long term. (Your ability to take risk is relatively high). On the other hand, based on your personality your willingness to take risk may be low. So, you will have to build a portfolio at a risk level that balances the two (Your risk profile).
In terms of asset classes, consider Large Cap versus Smaller Cap, US versus non-US, Developed versus non developed. For bonds, you should consider interest rate sensitive versus other less interest rate sensitive. US versus non-US.
Portfolio construction really depends on your beliefs, ability and how much time you want to or are able to spend (In addition to your risk profile). You could have a broad allocation to the above asset classes and simply rebalance (I recommend yearly and if there has been a 5% or more deviation in allocations) or you may want to supplement the broad allocation with 'tactical tilts' depending on your views. In your case, it seems the former is better. The exact allocation to stocks versus bonds really depends on your risk profile.
Then there is the question of whether you want to use active managers or passive managers. If you have a strong view against active, you may want to stick to passive vehicles like ETFs. Although, the press has more or less dismissed the ability of active managers to add value- it is not that simple. If you put in the work you can find talented managers. If not, stick to passive investments such as ETFs
Diversifying risk should be a top priority. ETFs are a great way to do that. Fighting inflation while targeting growth is important. Consulting a financial advisor on your options would be a great idea. Learn more about ETFs here.
Determine how much you can tolerate losing. Are you going to need any of it? When? For what? The sooner you need some of it and the more of it you need, the less risk you can afford to take. If it is a modest sum, and you can afford to take some risk, consider a diversified mutual fund. If it is half a million or more and you can invest for the long term,, then you can look into buying individual securities in a diversified portffolio.
First, make sure that you have money set aside in a savings account to cover at least 3 months' expenses plus any short term expenses you know are coming (vacation, car repair, etc.)
If you have a retirement account at work, consider investing there and using your inheritance to back fill the money missing from your paycheck. There are great tax benefits when you save money in a 401(k) at work. If you don't have a work retirement plan, consider opening a Traditional IRA or Roth IRA and contibuting $5,500/year there. You can buy diversified mutual funds through any of these retirement plan options.
If you just want some ideas for diversified funds that you can take out at any time, consider mutual funds that invest in several areas of the investment markets at once. Target Date Funds are a good start for beginning investors.