score:4
That's a lot of questions!
Should I hire a car or are there tours available to tourist areas? You probably don't need a car, the public transport in Tbilisi is pretty efficient, and when it's not it's still interesting :-)
Are there regular bus services? Yes, there is a metropolitan bus service. Most locals use the minibuses that you have to wave down. If your Georgian is rusty, this isn't a great option, but a surprising number of drivers do speak English. You have to request a stop, and request it before you get on, otherwise you may get an unexpected tour of the city before you get off!
and what is the rail network like? Clean and efficient. There's tons of kids acting like hoodlums, but in my experience they're harmless. Watch your stuff though!
კეთილ მგზავრობას გისურვებთ!