My wife joined me on a business trip in Israel recently. Our hotel in Tel Aviv recommended a tour operator with numerous packages available, including both group tours and private tours to most destinations. We booked one group and one private tour.
Group tours can be frustrating because you are at the mercy of the slowest people. Even with a small group (ours was 9 guests) there's usually a person who can't walk fast, a person who needs long bathroom stops, 2 people who disappear into every gift shop they pass, etc. Go with a big group and it's even worse. Like an elementary school field trip you could spend half the day just getting on and off the bus and counting heads to make sure nobody's left behind.
Private tours avoid all the frustrations of group tours because it's just you and your guide. You decide what to see and at what pace; the guide offers suggestions and takes you through everything like an expert. The downside is price. Ours was 500 USD from Tel Aviv for a full day. Comparing notes with friends who've visited separately this year that seems to be the going price. Your hotel can help with recommending a specific operator and making the reservation.
If I were doing it all over again for the first time I would seriously consider a mix of self-guided touring and free or inexpensive walking tours. One friend toured Israel this way on her first visit and really loved it. I considered doing the same but felt I didn't have enough time to plan so I went with the guides. But after 2 days I ditched the packaged tours, canceled my remaining reservations, and struck out on my own. I wish I'd done that from the start.