Hi Bonnie.
I'm not sure why you don't feel safe using a cellphone... but I guarantee you they are much more secure than the care-free analog days. Plus, some communication protocols are tower-only, which means phreaks (that's phone freaks... people who hack telecommunication stuff) would have to attempt to intercept within the location of your cellphone towers. Some are satellite based, but um... I don't know anyone that can hack at that level yet... except Uncle Sam of course.
Contrast that with, say, the internet where anyone from anywhere on the planet can attempt to hack anyone else on the planet. So, in terms of accessibility, the internet is much less secure.
Security is a bit of a balancing act. Too little is bad but so is too much. Much like budgeting or investing, how much depends on the individual's real world needs. But the question I am wondering is why you need a high level of phone security? Even someone who is as security-conscious as me hasn't seen the need of it yet... but I don't know you or your situation so I really can't say for sure.
Of course, if you still prefer landlines, I don't see anything wrong with that either. They certainly will provide you greater security at a reasonable enough price.
While we're on the subject, it's worth noting that using a debit card is not as safe as it using a credit card. Most credit cards offer superior fraud protection, whereas debit cards will draw money straight out of your bank account.
In fact, I have a cousin who just found out that he got defrauded $3000 and is going to have trouble paying his mortgage this month because of it! That's because he uses a debit card for all his transactions. I recommended that he (and you) get a small limit credit card and use that from now on. Not only will the credit card protect you, but it can also help improve your credit rating.
That's my opinion anyway. Whatever you decide on, I guarantee you that you are actually at more risk being on the internet and using a debit card right now.