If you're headed to the Magic Kingdom, it depends where you are staying at the Polynesian- the TTC is about the same distance from Rapa Nui and Tahiti to the GCH. The Express Monorail tends to be very busy in the mornings, but other than that it is usually a quick trip that will usually shave a few minutes off your journey (vs the resort monorail).
For Epcot, I'd recommend trekking over to the TTC no matter what building you're staying in. Since the resort monorail travels in the opposite direction of the TTC, you'll have to do just short of an entire circuit to get to the TTC- this takes an extra 20 minutes over the short walk.
Monorails start at 7:00 each morning unless it's an EMH day, where I believe monorails begin operating 30 minutes prior to park opening. Check with guest services at your Disney resort for exact times. Note that the express monorail may not be in operation for MK EMH.