Do any of you have experience with a long-term care annuity?

Why not just invest wisely and long term. See an advisor. The down side of annuities is if someone dies early there is a tax liability. My brother died at age 62. As executor and the way he left that to 2 beneficiaries they were advised to take payments over 5 years so that the tax hit was less. If money came from stocks or mutual funds, they would have inherited on a stepped up basis

www.bogleheads.org for the best UNBIASED financial advice.

You need good and solid financial advice. Annuities are sold by insurance companies and their salesmen support themselves on commission. They make money selling them. They aren't always the best investments, dependent on your particular situation.
Long Term Care Insurance is costly, and often tricky when you try to access it. Being self insured (read, having a lot of money) is the better way to go. The question is how to get there.

Dependent on age you will want good diversity of investment to make yourself financially self-insured. And that happens over a lifetime unless you strike gold or oil.

Do you listen to Dave Ramsey's podcasts/programs? Have you ever attended his seminars? You will get for little money a really good basis in how to save and how to invest. He also has great books. He is faith-based, and I am not, but I truly admire this man. He also has a list of trusted financial advisors. If I needed help that's the route I would go--my starting place. Because you would meet people who could help support your plan.

Right now there are good interest rates and you can get 5% on your savings at FDIC insured bank. Chuck your savings away a while and let it grow while you educate yourself before trusting a salesman from an insurance company would be my advice. He's making a commission. (as in "follow the money". I am not saying annuities are wrong. I am saying they are not for everyone.