For btc from wallet to GDAX about 20-30 minutes depending on how busy things are. But, that was a while ago and I think the tx are much faster now. Sending ltc has always been much faster and cheaper. Again, it's been a while and I think btc has caught up. There is a very small fee to transfer from wallet to GDAX. Very small. I lost a ton in fees to CB before I figured out what the hell I was doing!
Caveat: If btc busts a 2-5k move up or down both exchanges can be down for awhile due to high volume. Never store your coins on an exchange imo. Exchanges are high value targets for hackers. MT. Gox comes to mind.
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