does the pedal feel firmer if you push once and right away push again ?
more over, given you have new parts, when the car is parked and ON, press on the pedal firmly and keep pressure on it for half a minute or so. repeat that three to four times. that will bed in the distance in the new pads with the calipers etc.
if the first scenario is present where the second push is always firmer, then open up the callipers and clean/grease the calliper sliding pins as well as the calipers inside where the pins slide. that ought to do the trick
keep us posted and good luck.
DOT 3 is just fine. no need to change to DOT 4. and bleeding isn't always the cure either. try the above first.