Prepare everyone for lots of walking. This itinerary takes you all over Helsinki.
Finland is very far north and can be quite chilly throughout the year. We last visited the town at the end of June, and it was cold enough to require jackets. Make sure you have warm clothes with you, as the weather can change rapidly.
If you are visiting in the winter, start at daylight. The days are short in the winter, and you'll only have about 6 hours to explore before dark. In the summer, it stays light until about 11 p.m., but the markets won't be open past 5-6, so plan accordingly.
Summer is a wonderful time of year to visit if you like sun and long days. Winter is gorgeous and special, but it can be harder with kids. The market is not open daily in the winter.
Most of the places visited on this itinerary are free, so there aren't opportunities to save money other than your choice of lunch.