Which mon to lead the Giratina party?

I do 3 dragonite 3550-3559, Rayquaza 3550 and 3500. Then Salamence 3514. Then two maxed shadowball M2. The two I did today had Shadow Sneak, 40, 38, 33 beat it with 45 seconds left. Dragons are best (virtually any real dragon), Mewtwo next best. I actually have another Ray at 3100, it was traded for so IVS so-so. Really easy choosing: dragon, dragon, dragon, etc

Lead with Gengar to give it a chance of getting an additional shadow ball off. As you say, Ttar is a tank, put it at the back.

See if you can grab a Rayquaza or two in trade, preferably for something very old that can go lucky. The dragons will be useful against Palkia too. Not so against Dialga, though.

Dont use SC gengar or SB mewtwo if you have dragons. Always lead the dragons, they are *FAR* better

I would lead with Gengar just because early on you have a higher chance of getting your charged moves off before getting hit by one yourself. If you put it in the middle it could get hit by a charge move right off the bat

As a rule of thumb put your glass cannon first and leave the tanky mons for the last spots to avoid or delay wiping out. Gengar may be able to shoot one more shadow ball by leading the party than by joining midway and being hit with a Charged move sooner

I have one rayquaza, but I can't be bothered powering it up when I already have 6 dragonite level 33+.

I would lead with gengar, followed by your dragons, then Mewtwo and last tyranitar. Guess that's your best way to compete for damage contribution with your current team. Starting when highest DPS and maintaining good pace when everyone else starts dropping theirs.

"I sort of know the first two moves from the boss hits harder but not sure how would that affects."
Either you didn't get something right, or I didn't get right what you wanted to say. The first two moves do not hit harder at all. What happens is that in the beginning of the fight, you know that the energy bar of the enemy boss is empty so it can't use charge moves. Later in the fight, if it has enough energy it will fire either a charge move or a fast move, the choice being made with a dose of randomness. What it means is that:
* You can't predict when you'll get hit by a charge move in the middle of a fight;
* You know that the first 2, maybe 3 moves of the enemy will be fast moves.
Generally, that means you can lead with a glass cannon because fast moves hurt less than charge moves. EXCEPT when you use Gengar vs Mewtwo or Alakazam, especially if the boss has confusion. Indeed, in that case, the fast move hits Gengar for super effective damage and when that fast move is confusion, it hits HARD. Especially annoying when Gengar takes neutral damage or has triple resistance towards the charge move! So, in this particular case, it's best to use another pokémon to tank the first two confusions of the enemy boss. But in general, Gengar is fine.

For Giratina: if it has Shadow Claw, lead with a dragon. If it has Dragon Breath, lead with Gengar.