You say you've never flown between cities in Europe before, but have you taken trains or buses in Europe before? This will help people give more useful replies.
If you have taken trains in Europe, there's nothing extra to know about the trains between Venice, Florence, and Rome, except for the tips about advance purchase, non-refundable, discount tickets. There are lots of posts about this; here's a very recent one: https://community.ricksteves.com/travel-forum/italy/confused-on-booking-train-reservations-and-tickets-by-website-help
For Cesky Krumlov to Prague, there are several bus companies. The bus is faster than the train - if it doesn't get stuck in traffic. And there's no bathroom on the bus. When mine took 5 hours (instead of the scheduled 3) due to road construction, some people had to hop out and go in the bushes.
Too much information? Maybe, but you asked. The good news is that my trip took place in 2007, so that construction is definitely done.
For budget flights, do a dummy booking for each option (up to the point where you put in your credit card). This is the only way to see all the fees and rules. Note that the legacy carriers can be cheaper in the end, since they can include things that cost extra on the budget airlines.
If your baggage exceeds the carryon limits (and on a budget carrier, it probably will), be sure to pay for checked baggage online, at the time of booking, or at least before you get to the airport. They charge more if you do it at the airport.
Ryanair requires a passport check, in a separate line, before they let you board. Look into the details of this so you're prepared (it's not reported to be hard, but if you miss this step, you could miss your plane).
Some budget airlines require you to print your boarding pass before getting to the airport - again, check before you get burned.
And if a carrier says it allows one carryon, they mean only one - not a carryon plus a personal item. If you can stuff your purse into your carryon and make it one bag, fine; otherwise, you have to check something.
Many of the complaints about budget airlines are from people who didn't read the rules, or didn't think the rules would apply to them, or didn't understand that the rules will be interpreted strictly (since this is how they make money). If they say the maximum size allowed is 50 cm, don't think they will let through a 51 cm bag; they will consider it oversize, and not only charge you as such, but a higher charge than if you had paid it in advance.
Again, a legacy carrier such as Alitalia or KLM is likely to have a more generous allowance for both carryons and checked bags, included in the base price. So, they can sometimes work out better in the end.
