2nd class is perfectly acceptable on Eurostar and it’s only just over 2 hours, anyway. If you’ve found special fares at www.eurostar.com then book them as soon as you’re sure of the dates. Eurostar is priced like an airline with only a limited number of “cheap seats” available on each train. When those sell out the price goes up. I would NOT wait to get Eurostar tickets. For all of you cities there will be a train or bus to city center from the airport. That’s almost always the cheapest way to get to town. There are a few cities where taxi fares from the airport are set by law. It’s remotely possible that 3 or 4 of you sharing a cab can get into town as cheap as on the bus — be sure to find out about charges for extra passengers and for baggage as what looks like a cheap taxi ride may not be. I only buy a reservation if the specific train I want to take requires one. It’s best to buy your reservation at the train station about a day in advance, but reservations are usually available up to 1 hour before train time. If you want to take a train that requires a reservation and don’t have one plan on arriving at the train station about 2 hours before train time. Save yourself a trip to the train station but the reservation for the train you want to take when you leave a city before you leave the station when you arrive in that city.

As for hostels, you don’t generally have to book very far in advance but it depends on whether or not you want to stay at a specific hostel or have some flexibility. If you’re sure of the place you want to stay in arrival city, I’d book it now as teens and tweens on school trips fill up some hostels in late May and June.