Hey there. I've been to Europe twice and looking to do another trip sometime next year.
For flights, definitely have to watch the calendar and your own personal schedule when you could take time off. Always book way in advance if you can, to get cheaper flights. If you wait within 2 weeks of flying, flights will be significantly more expensive. I've used Norwegian a few times since they are reasonably affordable and my destinations were in where they would fly to.
For Shelter, depends on what you find comfortable, your price point, and how long you are staying at each destination. There are community hostels where you get your own rooms but other amenities like bathroom, shower, and hangout area is shared. They are usually on the cheaper price point. I usually stay at a certain place for a week and prefer just to get an airbnb and live like the locals. Would usually come with a kitchen, if I wanted to cook. For airbnb, the price will also depends on the neighborhood. Some neighborhood is much more expensive than others. You would have to shop around for what you want to afford and look at the metro and bus lines. Leading into transportation, you always want to live in an area where there is sufficient subway or bus lines for easy transit to areas you want to visit. You should never need a cab. Some cities might have metro tickets that are dailies, weeklies, or you can pay per trip. Paris for example, you should get the metro card (that would have your picture on it, but you are require to bring them an airport style photo) and load the card up with funds for your commutes. So maybe bring an airport style photo just in case you do go there or some other places might want you create a photographed metro card.
For currency, plan ahead. Ask your ban to get you a certain amount of money for each country you want to visit. Most European countries will accept Euros. Certain ones will only take their country's currency. You will have to do some research. Take enough where you think you might need it just in case and for how long you will be there for. I stayed in Sweden for about a week so I took $300 USD worth and converted to Swedish Kronas. That might be a bit overboard. $100 would probably be fine or less. Most places will accept your visa/mastercard and you should always pay in the local currency when asked. Your card will automatically convert for you, otherwise you will pay additional fees if you choose your own currency. For bank conversions, at least in the US, it may take up 3-5 business days to for them to order your currency. So don't wait until the last minute. If you didn't plan ahead, you could also convert at the local airport if you are desperate, though fees may be higher. For tipping, most restaurant places you can tip 1-2 euros and it should be sufficient. Depends on the country and their tipping habits. I have the tipping habit of an American, and that's not always needed for where you are. Definitely should probably google search this each time you're in a new country for local tipping habits. If you do those free walking tours that some cities will have. They take donations if you want to tip, but in cash. Those are really fun and cheap entertainment if you like hearing about the city's history.
For season, it's whatever season you feel like going. Summer season is always going to be the most crowded. If you like crowded lively streets, then summer. If you hate people and prefer the cold, then winter. Summer season travels are usually more expensive unless you are traveling during winter holidays, which is probably even more expensive. I prefer to travel during the summer, especially if you are doing nature spots like Plitvice Lakes where it's optimal to see it during the summertime. For optimal traveling, especially if you are backpacking and hitting multiple destinations. Don't pack a lot. You should have one bag that you could carry on your back comfortably, don't lug around wheels., and if you need to take your laptop with you and other essentials, it can be done in a laptop backpack as well. I sometimes have a bag for my cloths on my back and my laptop back I just carry it in my front. Don't do wheels and don't pack so much. Especially if you're thinking of getting some things back like souvenirs or gifts for families/friends. Get those efficient bags with packing cubes. Traveling bags are a good investment if you plan to travel a lot. Learn to pack.
I forgot to mention, if you do airbnb, convenient to find a place with laundry. Most European places won't have a dryer. You have to hang dry it. If you do hostel, they may not have laundry rooms. You will have to go to a local laundromat, which may require coins. This is where having converted currency from your bank helps, see if you could ask for some coins as well just in case. Often times, you could also ask the locals to break your bill for you as well, or the laundromat might have an attendant that can help you.
If you're hitting multiple cities and countries. Plan ahead your routes. That way it's efficient and cheaper. Sometimes you may opt to go by ferry if you're crossing the Aegean Sea for examples to go on the Greek islands. You can book the ticket online and find where on the map you need to go to pick up the ticket. Sometimes you may need to fly to the next destination. Often times if the cities are only a few hours drive apart, you may also consider taking the bus as well. The bus option is super cheap from one country to another, it just costs more time and the bus bathroom is not an attractive option. So don't be drinking so much liquids. They do stop every few hours for restroom breaks. Have your passport ready for border crossings. Some places have 20-60 minute wait time. Having local cash on hand is useful for these stops. Some places may only take cash. Be conservative with your cash, always pay with your card where you can. But on the last 1-2 days, spend the rest of your cash. I like to collect foreign currencies, so I usually keep a few coins and some bills.