First of all, never buy one of those variable annuities, they are pretty much scams, with at least 3% going to commission and fees every year.
Secondly, annuities are good for those who want fixed income or longevity insurance like a QLEC. The returns are very low. If you are afraid of running out of money, you can buy a QLEC (you can look it up) that starts say at 85 years old, which is the lastest age that you are allowed to start with tax deferred money. This is to ensure that you have a steady income stream that is not inflation adjusted, starting at 85 years old or whatever age you choose until end of life. It will be to supplement Social Security income.
I don't think it is a good fit for you to start one when you retire due to returns of about 5% if you buy a fixed period term annuity, say a 10/20-year term. If you buy a single life annuity, you don't really get breakeven for at least about 20 years.
On the other hand, we have large enough retirement investable assets when we retired that I bought 2 fixed period income annuities to supplement our income, to create a pseudo pension for ourselves. It was only about 12% of our investments.