You recommend never lying to police, but what if they ask if I have illegal items and I do? Should I admit to having illegal items? Should I lie?
This is a tricky situation. Of course you should never admit to having illegal items, but you also should make every effort to avoid lying to police. You're always free to remain silent, and police may not hold your silence against you as evidence of wrong-doing (especially if you assert your rights with confidence).
The simple fact is that making false statements to police officers is a crime in and of itself in many jurisdictions. Regardless, this is a rare situation where some experts secretly recommend lying. The main reason to avoid lying is because police are good at detecting it, but in this case that doesn't matter as much because you're already a suspect. Personally, I look at probing questions like a police officer seeking consent to search my brain, and we all know how I feel about searches. I highly recommend watching this video lecture about why it's often best to just keep your mouth shut!
No matter how you respond to a police officer's questions about any contraband you may or may not have in your possession, the most important thing is to be prepared for the inevitable next question: "Do you mind if I search you / your car / your home / your bag?"
Always refuse the search, and remember that you can't get in trouble for asserting your rights properly!