What would be the advantage of using an alkyd based polyurethane for the first coat and then switching to a water based polyurethane?
Aren't you just inviting problems with adhesion between the oil and water based films by doing that?
You said: "use water or oil poly?".
You should be aware that there are more than a few different kinds of water based polyurethanes, and they're not all similar in their properties.
If you're going to be doing this work yourself, then an oil based polyurethane will give you a very durable finish on your floors. Water based polyurethanes, I've been told, aren't quite as durable, but have the advantage that they don't yellow with age and you can put more coats on faster because their drying time is shorter.
The yellowing of an oil based polyurethane (or all "oil based" coatings for that matter) is significant only in low lighting conditions. If your floor gets lots of natural sunlight, either direct or indirect (as in reflected off a ceiling or wall or both), then yellowing won't be significant. That is, you'll never notice any yellowing except perhaps under furniture, but that yellowing will disappear within a few weeks of moving the furniture. That is, the yellowing is completely reversible once the yellowed coating is exposed to direct or even indirect sunlight.
Also, you should be aware that you can get MUCH more durable coatings for wooden floors than an alkyd based polyurethane.
Bona makes a catalyzed isocyanate based polyurethane for hardwood floors called "Traffic", which is about 3 times as durable as an alkyd based polyurethane hardwood floor finish and doesn't yellow. They call it a "waterborne" polyurethane because the isocyanate prepolymer is suspended in water. You pour in the catalyst, shake the jug to mix the catalyst into it and then spread the stuff on your floor.
Wasser makes a clear moisture cure isocyanate based polyurethane coating (which doesn't yellow either). This one is about as durable as the epoxy floor paints often used on factory and warehouse floors. With moisture cure polyurethanes, you just spread the stuff on the floor, and it reacts with the moisture in the air to form urea linkages. That is, this stuff is actually not a poly"urethane" at all. It's a poly"urea" because it's urea groups that form as the stuff cures, not urethane groups.
I'd contact both Bona and Wasser to find out if pine is too soft a substrate to put their coatings over. (The harder the coating, the harder the substrate needs to be to properly support it.) Also, I know Wasser makes a clear moisture cure poly, but I don't know if they recommend it as a clear finish for wood floors, tho. Check with them.
And, I'd recommend you hire a company that refinishes wood floors to put either one of these coatings on. Once you mix the catalyst into the Traffic, then the stuff is going to harden up on you regardless of whether you run into problems or not, so you need someone with experience using Traffic to avoid potential problems. Also, I've been told that moisture cure coatings stink to high heaven as they cure, but I don't know if I was misled, or if it's only certain ones that stink.
PS: you don't need to know the rest...
(Oil based "polyurethane" hardwood floor finish is best thought of as an ordinary alkyd (or "oil based") paint without the coloured pigments in it to give it colour and opacity. Additionally, the "polyurethane" resins in a hardwood floor finish are harder and stronger than the alkyd resins in oil based paint ONLY because the "polyurethane" resins have urethane linkages inside them. Those linkages act very much like the roll cage inside a racing car, making the oil based polyurethane resin much harder to crush if you could squeeze one and much stronger if you could try to stretch one. So, polyurethane hardwood floor finishes are harder and more durable than oil based paints only because their resins have urethane linkages inside them, whereas oil based paint resins don't.
With isocyanate based polyurethanes (which both of the above two coatings (Bona or Wasser) are, what you'll have on the floor is an entirely different thing than an oil based polyurethane. It will be a plastic made up almost entirely of those urethane (or urea) groups. Since those groups are very strong, the resulting film is very much stronger and more durable than an oil based polyurethane (which has far fewer of them). This is the reason why isocyanate based polyurethane coatings are so much more durable than alkyd based polyurethanes. It's because urethane and urea linkages are very strong, and the more of them you have in your coating, the stronger and harder the coating.