Transport in Italy

Trains typically do not sell out. However on long distance high speed trains you can save money booking in advance.

Just go to www.trenitalia.com and look up the routes your are interested in. Look up for eg. today to see what is normally available. If the only price you see is "ordinaria" then you know you are looking at a local train where the prices are always the same. Trains are mass transit, used by people to go about their daily business. People commuting, going shopping, visiting family or going out do not book trains in advance. The same for local mass transit. In many places you can even just tap in and out with your credit card on local buses. But that varies from place to place.

For long distance trains you will see several price levels. The "base" level is what you pay if you buy a ticket at the last moment.

It is difficult to respond to your questions without knowing where you are planning to travel. Train vs. bus depends upon where you are traveling from and where you are going. Taxis are readily available in large cities and town and not generally available in small towns. Taxi apps are generally city specific. Buses tickets can be bought on board with the "tap and go" payment method.

A good guidebook and some research will serve you well. There are usually suggestions for the best method of travel contained therein.

Italy is a great place to visit. Try to plan your first visit with the expectation that you are on a scouting mission, scouting for destinations for future visits. It's a place that demands more than one trip.
With respect to travel, I use trains and also rent a car. Where you are going makes a big difference. If you are going to Rome, Venice, Milano, Florence, a car will not be very useful. You can use trains to connect those places. The buses, trolleys are adequate and better than cabs for the most part.
I book train tickets a day or two before I travel. I don't like to box myself in and unless you are super fussy about seating, I would not get too stressed about advanced tickets.
If you plan to travel in the countryside, a car is absolutely the best way to get around. We like to stay in Agra Turismos, most of these are in the countryside. You could make yourself crazy trying to get to one by bus and cabs would be very costly.

YMMV

You have to ask better questions. For me, driving a car was the most convenient way. For someone else, another method may be more convenient.

No one here can read your mind and give you a magic answer that is going to solve your problem.

Not a good idea to ask this question when you are going in July and it is the day before July.

Where exactly are you planning to go? Public transport isn't the same everywhere. Whilst the train is usually the best option between cities, it's not always the case. It's really hard to answer general questions on transport since it is so dependent on what cities/towns are on your itinerary. I'm not even going to get started on transport strikes!

Are you writing a report on this? Because much depends on where you are headed..why not let us know the destinations.

Hello :)
I agree with everyone. We need more info to help you.
But short answer:
Hilltop villages in Tuscany. Rental Car
Big Cities to Big Cities. Train (The fast one ;)

Have fun.
Sincerely, Joe :)