Hi!
How to Play in Gigantic
Simple: don't play in gigantic.

More seriously: there's a limit of ~200 habitable planets I can stand in a game. Anything above that kills fun, because there's too much micromanagement (MM) involved. All my gigantic games were rare or uncommon stars&planets, but I was still not happy, because it took almost forever to move ships from my production centers to where they were needed.
how do you know when to stop expanding or when you've expanded enough since there are so many worlds?
You need to constantly watch your economy: when your treasury starts vanishing rapidly (-500BC at 59% tax), it's already too late to stop colonizing. IMO -100 BC at tax level that makes 40%+ approval everywhere and with 1000-2000 BC in treasury is a sign to stop.
And what technologies should I go after that specifically cater to gigantic maps?
Gigantic maps tend to play less agresively, so you have more time to develop your empire. Take it, and do the task properly. Only when colonizaton phase ends for AIs, you need to develop some warfaring technologies to make yourself less attractive terget. You don't need to build serious warships until AIs start using engines on their warships: whatever they send at you before that, you can make awfully obsolete when it actually gets to you. Range upgrades you don't need so much, because the default range in gigantic is about 3 sectors, and there's a hard cap of 7 sectors. What you need in those wast distances is speed. And luck for avoiding "speed reduced to 5" event.
BR, Iztok