The 'where' in the title refers to what type of account should you invest in, not what to actual invest in. This is a very confusing topic to newcomers. A 401(k) is not an investment, it is a form of an account that has preferable tax treatment. The actual investments are offered within your 401(k) plan and take on the traditional stock, bond, real estate, cash flavors mentioned in other articles. This article is only on the companies and types of accounts that are available.
Retirement accounts generally offer the best tax treatments, considering they are used as a way to assist elderly Americans and they are, by definition, long term investments. The major types of accounts fall into two major categories: 401(k)s and IRAs. A 401(k) is an employer-sponsored plan, where you are allowed to get beneficial tax treatment for saving using the plan. A traditional 401(k) allows you to place untaxed dollars into your 401(k). When the money is eventually withdrawn, it will be taxed just like regular income. A Roth 401(k), on the other hand, taxes the money you place in. When you take it out, however, the money is completely tax-free. SIMPLE IRAs are a tax-deferred employer-sponsored IRA (kind of a mix), where the contribution limits are lower than traditional 401(k)s.
Where the above examples are all employer-sponsored, Roth IRAs and traditional IRAs are up to the individual to create. The annual limits for contribution in 2016 are $5,500 for those under age 50 and $6,500 for those 50 and older. There are income requirements to contribute to a Roth IRA and to deduct the contribution for your traditional IRA (2016 listed here). These offer more opportunities for individuals to defer taxes than a traditional 401(k).
Many employers offer a 401(k) "match" on contributions. If you make a contribution to your 401(k), your employer will then give you more money for the account. At the risk of oversimplifcaiton, everybody should contribute to their 401(k) to obtain the match at almost all costs. After this, many would prioritize paying down higher debt before investing more in retirement. For the extremely high savers (those able to outearn their expenses by a lot), the combination of 401(k) and IRA is possible, offering a lot of tax savings specifically earmarked for savings.
The IRS has carved out plans in the tax code to help parents save for education costs with tax-deferred spending. Generally, the contributions are only tax-free when it comes to state taxes, and many states do not allow deductions so be sure to check your local laws. This is a good guide on the availability of 529 college savings plans. Just like 401(k)s, there are many different 529 plans and some are better than others. Look for options that provide low expense ratios in their funds and a lot of options so that you can properly diversify.
Most other accounts fall into this category. After you have satisfied your retirement savings, you will want to put extra retirement savings into a taxable account. Or, you are looking to save for something else, such as a house in the next few years. This is where taxable accounts come into play. There are many options for taxable accounts, but my personal favorite is Wealthfront. They take your personal risk profile and tailor it for a well-diversified portfolio. The key difference to taxable accounts is, well, they're taxable. This means that every trade in them is subject to tax laws, such as short-term or long-term capital gains. There are some forms of investments, notably tax-free municipal bonds, that provide tax-free returns. If you own these funds and have a taxable account, they should be in your taxable account. Their benefit is lost in a tax-protected account since every investment is tax-free. You could theoretically hold all taxable forms of investments in your tax-protected accounts (like IRAs and 401(k)s) and then only hold tax-free municipal bonds in your taxable accounts. You then are subject to extremely limited tax liability.