First, let me toss a huge disclaimer on what I posted before:
That's what I did. It worked for me. Once. With the way that aquaria are so "individual", I am not that confident that I could duplicate those results if I repeated the exact same steps. That is, as they say, "your mileage may vary".
Ok, now that that's out of the way...
I, personally, would get in the mindset that you're still "doing a cycle" on a new tank, even though you've got some significant help. If you add fish right away, they can certainly still be stressed and/or die.
On the other hand, once you introduce some 'good' bacteria, it'll need food, or it will die. That means you should add a source of ammonia. You can go with either a 'standard' cycle with fish, or a 'fishless' cycle, whichever you're more comfortable with. Personally, I'd use fish.
If you go with a 'fishless' cycle, make sure you have a solid understanding of what's involved, before you start. Among other things, it could prevent a stressful scramble around town, looking for 'pure' ammonia ... on a Sunday, no less.
That said, I'd probably add the first dose of ammonia right after filling the tank.
If you go with fish, then what I'd probably do is something like this:
Set up the tank tonight, and fill it with water (use old water if you wish). Let it run all night, to make sure that you have no obviously defective equipment, and to let the heater stabilize the temperature. Then, in the morning, do your gravel transfer, and then try to introduce your 'cycling fish' within a few hours.
A couple of other things you may want to consider:
* The old gravel isn't 'free'. That is, remember that if you transfer gravel from the old tank, you're removing beneficial bacteria from the old tank, too. If you take too much out, you run the risk of 'crashing' the old tank. The risk in your case may be slightly higher, since you just changed your filter media (less if you just changed the sponge, and left your Bio-surface things in). Keep an eye on the old tank's parameters, too, for a few days.
* I'm not sure if I'd intentionally add algae to a new tank. I'm not certain if the algae itself is a good bacteria bed or not.