I moved pianos way back when.
AFAIK, piano tuners belong to a guild, so there’s so many years of apprenticeship, certification, and so on. I’m not saying one’s as good as the next, but there are standards.
Three healthy men and a truck theoretically should be able to move a 4’ upright. Going upstairs you’ll have two pushing and one steering. If the stairs are tight and twisty it’s going to be a struggle even for pros. Basically it involves a series of moves where the piano is positioned for the big push, then everybody joins in for the heave ho. It’s a real teamwork job.
If you’re renting the truck and all the other stuff you’ll need to make the move (dollies, blankets, ramps, straps, etc.) you might not be saving all that much over having pros do it.
The thing with moving pianos is you don’t carry them. You either put it on a moving dolly and roll it or you slide it, preferably using a skid specially made for piano moving. The little wheels are mainly for fine-tuning placement. Also, you don’t always have to lift the whole thing off the ground to put it on a dolly. You can tip it and have someone place the dolly underneath, flat against the bottom of the piano.
Before moving the piano, be sure to disassemble it as much as possible. At the very least the legs ought to screw off if they’re not fixed at the bottom.
Securing it inside the truck should be done with straps unless someone in your crew is a genius with knots. Secure it to the forward wall to keep it centered in the truck, unless you’re counterbalancing it with other stuff in the truck.
Lots of stuff to consider, but it can be done, although three flights of stairs can be a lot, depending on how they’re configured. You run the risk of doing more harm to yourselves or your house than the piano. They’re pretty solid.
Your friendly neighborhood piano dealer should have recommended piano tuners. It wouldn’t hurt to ask about how much it would cost to move the piano, either. It doesn’t have to be one of theirs. Bottom line is it’s a free piano. If it’s any good and you want a piano this is a real windfall.