Having traveled by myself & with groups, in a number of countries… I'd highly suggest that your first trip to Israel be with a group. It will be that exciting, & not the cattle car feeling most group tours give you.

Here's a few factors:
~ Unlike most countries, the sites to see aren't logically concentrated in the downtown area within reasonable distance of each other so that you can wander through them. I assumed incorrectly on this & wound up quite frustrated. These sites were built for people to use many millenia ago, & are just not logically placed!

~ So, You'll see more & learn more on the group tour. It's not well designed to pick up an understanding of any site just by going. You will see & learn much, much more with a guide than if you go by yourself. I tried tagging onto the backs of groups to hear snippets, but it didn't work well the way it does in other countries…just too spread out & noisy.

~ The tours will arrange types of events you can't get on your own. On a tour I also took on my last trip (I was there a month & did more than one thing), we met with army majors & IDF soldiers, a high level peacenik activiest, & more. I found I got more info out of those (often casual) conversations, than efforts on my own. Seriously, I usually do better on my own in traveling at learning things, but here it wasn't that way. You just can't get the access on your own both to unusual meetings & to sites to see. Some sites are for groups only - which took me by surprise - & need advance reservations. Also everything is so chaotic, that you can't just look it up in a travel book & plan it. The sites aren't open at the times listed in the books, then a holiday appears… Once you're a little familar it works well, but a group really does help on the first trip.

~ Safety-wise, in Jerusalem, I wouldn't wonder off without an idea of where to wonder. E. Jersualem isn't the safest. Not a big deal, I got myself good & lost, but I bet your parents will care to worry less if someone's in charge of you.

~ Finally, take your concerns to birthright itself. There will be free times at a stretch on the trips that meet your needs. Research what you would do on your own, & see how it compares. Don't just read, but get to the nitty gritty of making any plans you would want to, to see if they truly work. Then make an informed decision. One or the other might be right for you. However, it's not as obvious a choice as it looks. I like wandering on my own, but if I hadn't already done a tour when I was younger, I would have missed the point of the place in many ways…and not even known it.

EDIT:
Maybe tack on a few days on your own at the end of the trip? Keep in mind it's hot, hot there during the summer, so you can do less than in regular temps.
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This site will answer most
http://www.thelivnotexperience.com/Pages/faq_fyi_livnot.htm
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