In addition to everything else that has been written:
I'm a single female, originally from England and have been living in Israel for decades. I feel perfectly safe going everywhere alone, even late at night (obviously one uses common sense and doesn't go alone down unlit deserted alleways, but that isn't specific to Israel).
Most shops take credit cards, but some small establishments aren't set up for it so you do need some cash. There are ATMs everywhere. Just make sure you have a 4-digit PIN, and tell your bank you are going to Israel so your card isn't stopped for security reasons (because the bank thinks it might have been stolen).
Public transport - buses mostly, but trains as well) - runs between all the cities. There are several companies operating the buses in different parts of the country (Egged is the biggest, but it doesn't cover the entire country), and you can get an idea here:
(Note that next Wednesday is Yom Kippur, on which public transport doesn't run at all, and it stops running early on the day before. This of course doesn't mean that on a normal Wednesday there are no buses ;-)!!)
There are also service taxis (sheruts) that are minivans, and their advantage is that they run on Saturdays and Holidays, pretty much 24/7 for some destinations.
Actually, no. The only sherut route that runs 24/7 that I know of is Tel Aviv to Jerusalem and reverse. There is no sherut from Jerusalem to any other city (that would be of interest to tourists) on any day of the week. From Jerusalem, if you want to go anywhere on a Saturday you would either need a rental car or else take a taxi. The exception is Palestinian transport to West Bank cities including Bethlehem. These buses run on Saturdays as normal. For that reason, Saturday is a very good day to go to Bethlehem. The buses leave from a terminal next to the Damascus Gate of Jerusalem's Old City.
Using public transport, in general you buy a ticket on the bus, from the driver (cash - shekels - only). The only tickets that need to be booked in advance are those to and from Eilat. And for a first-time visitor with only two weeks, I wouldn't recommend going to Eilat, which is really not much more than an overdeveloped beach resort. If you're going by train, you buy a ticket at the ticket window in the station, a few minutes before you travel.
Jerusalem now has a light rail (tram, streetcar) running through the city centre. Tickets for this are bought in a machine on each station, and need to be validated on the train as soon as you board. And public transport tickets within Jerusalem are valid for 90 minutes on any combination of city buses and light rail.
a target for robbery, kidnapping, rape, or pickpockets
Practically unknown in Israel, provided you use your common sense. Don't walk around with a wallet sticking out of your back pocket, don't leave luggage unattended - although if you do, it will be blown up by the bomb squad as a suspicious object, rather than stolen! Israel is very security conscious. You'll see lots of soldiers everywhere. This doesn't mean that anything in particular is happening. Most of them are travelling to and from their bases, and they are there to keep us (and you) safe.
Any further questions, just ask!
