When it comes to motor oil, you’re going to get a dozen answers and opinions. It all depends on your diving habit, type of oil/filter used, and how much money you’re willing to spend.
Well said, and that about sums it up.
So, here's another opinion. Since you just got the car and aren't sure if oil changes have been handled adequately and consistently, not just the intervals but the oil and filter quality and the previous driver's driving habits, I'd do your next change (including filter) fairly early, say 1000-1500 miles, and save a couple ounces of the oil you drain out.
That way, if there was an excess of contaminants when you got the car, where the filter was at its filtering capacity and the additive package in the oil had done all it could do when you changed it at 125k, the early change after 1000-1500 miles lets the oil and filter "catch up." After that, go to 3000 mile intervals.
You save some of the oil (and do the same after the other oil change) in case you want some analytical data to fine tune the oil change interval by sending your oil sample to a UOA (used oil analysis) lab. Since that costs money to do, I assume you'd rather hold off. But if you want data on the condition of your engine for its mileage, and whether your change interval is right, that would be something to look into. Google "used oil analysis" if you want more info to decide for yourself. There are several labs which do this, and you may decide it's not worth it to you. Just raising it as something to look into, since you're starting with an engine with unknown history (no matter what the previous owner said).