I am familiar with the basics and what is fair game to play in certain scenarios. But I'd go to megamanlan on the forums about anything advanced because he actually plays YGO.
I know at least there are normal spells, normal traps, quick play spells, and counter traps. Normal spells are slowest (and most monster effects) at 1. Traps and quick play spells are 2. Counter traps are 3. Some monster effects can be speed 2.
Chaining effects is like Redemption's battle phase and playing Enhancements. You might start by playing a speed 1 normal spell (or, say, Drawn Sword; a battlewinner GE). Then, your opponent has the opportunity to respond, but they can only play something with a speed 2 or higher; ie a quick play spell, trap, certain monster effects, or a counter trap. In Redemption these would be interrupts. The opponent then has the option of playing something of equal speed or higher. If speed 3 is played, then only speed 3 can respond. There is nothing like this in Redemption.
YGO you can chain just about anything if you follow the speeds. It goes by the last card played, then checks if the card played before that resolves after it does, and so on until you check if the original effect resolves after all that. You don't have to negate the card to chain to it- For example, the opponent plays Call of the Haunted (continuous trap that special summons from the GY and keeps the monster out while either is face up). You could chain MST (quick spell that destroys a spell or trap) to destroy the CotH, thereby destroying the monster. However, you would still get the monster's effect since MST didn't negate CotH's activation. At least, this is how I've always understood it.
If I explained it poorly... someone else can probably do it better. I haven't played in years or even at a high level at all.
It's basically Redemption initiative, only some cards cannot be played in response to others for being 'slower'. A big difference would be that if you played an interrupt + band in Redemption and Redemption followed some sort of speed rules, the banded character's ability might not activate if it was 'slower' than speed 2 or 3 (but, again, there isn't a speed 3 in Redemption).