We travelled from Ebbsfleet last week. You go through passport control before you get through to the waiting lounge (that's both French and British), so you don't do any further checks.
When you descend the escalators(or lift) to the platform you arrive pretty much in the middle of all the carriages, all the carriage numbers are clearly marked on the platform floor. When you find your carriage there are luggage racks at either end and Ive found the ones upon entrance are often filled up from those who boarded at St Pancras, so don't panic, you'll probably find the luggage rack at the other end of the carriage to be empty. There is plenty of storage above the seats for coats and smaller bags as well.
If you booked your tickets direct with Eurostar you can always change your seats online near to your departure dates and try to make sure you have empty seats near you, you then may not have to have the toddler on your lap. Obviously if the train is full you may not have that option but worth a try.
We always select our seats within a carriage or two of the buffet one so we don't have so far to walk if we want anything, there are 2 and they are marked on the seating plans
