We have moved several times over the years and never provided them food. Water makes sense, particularly bottled water which is portable, doesn't spill since it has a cap and they can carry it with them or set it down while doing their work. When you first arrive at your new location, you likely wouldn't even have any food and they may not have yet hooked up the refrigerator. Experienced movers know how long they will be at your house either packing/loading/unloading the truck and they tend to bring their own snacks with them. None of the major companies we ever used mentioned anything about company rules about what you can/cannot provide. Food is more challenging since movers tend to work non-stop and aren't likely to stop for 30 minutes to eat a meal.
Our experience has been with boxing up items which tends to take the longest time, they will leave for lunch (for example) and then return to complete the packing.
Only if they do something over and above for you would I consider tipping. (For example, if the mover doesn't routinely hookup things like a washer/dryer but offers to help.) They are workers at the moving company and get paid by their employer. To me it isn't any different then hiring a maintenance person to fix something. I don't think they expect me to tip them for doing a job they were hired to do and are getting paid.
Certainly think tipping at the START of a move is a bad idea since you create this expectation of further tipping. The person who comes to your home to provide the original estimate should also factor into the costs how long things will take, if they need to bring heavy items up flights of stairs, etc. That is all part of what you are paying them to do as part of the move.
With most of our moves, there also seems to be one person during the actual move who is in charge and it could be awkward tipping some but not all of the workers. I just don't see that as an expectation for the typical move.