My tank is finally cycled (phew)

After a small hiccup, I believe my 10 gallon is finally cycled. It's processing 3-5 ppm of ammonia in 24 hrs or less, and I'm at 0 nitrites as of yesterday.

This is what I want to put in the tank -
3 glowlight tetras
4 harlequin rasboras (if I can find them again)
3 cory catfish.

I was thinking of putting in the tetras and rasboras all at once, then adding the corys a week later. Is this too much of a lag time between adding fish?

I don't believe I am overstocked at this amount of fish, am I right?

Anonapersona, I'm going to do a very large water change, and probably only leave a gallon or 2 of water in there, so about 80% change. I'm also going to get a nitrate kit, but I think that large of a water change should be enough. We'll do it the night before we go to the fish store and use AquaPlus as a conditioner. This way the water can come up to temperature slowly.

I started fishless cycling on Dec 12th, and I thought I was done last week. Turned out I wasn't adding enough ammonia, only 1 ml, and when I went to do the test by adding 5 ppm overnight, I started getting nitrite spikes again. That was on January 14-15th.

What I did, on the advice of the good folks here, was bump up
the ammonia to 3-4 ppm and start testing.

So all told, it's taken about 5 weeks, using only an ornament from
my friend's tank to start with.

Not so bad for a complete newbie, I think.