New tank cycle

I know this has been answered a million times, but bear with me. I have a 40 gal tall that I just set back up after 2 years. I have (2) 5" true SAE's in a 10 gallon that I want to put in the 40 along with some new mates.
If what I am reading right on this site, I can take the established media from 10 gal filter and speed up this process? I read the sticky, just want to make sure I understand.
The 40 has been running for about a month. I did a fishless cycle with some gravel and plants from existing tank. I show no ammonia, nitrites and 5 on nitrates right now.
Can I transfer the filter media and fish at the same time? I have had these 2 for 7 years and won't do anything to risk them.
Then, what would be a great addition to the tank. Schooling fish that are hardy and interesting. I had black skirt tetras with them for years and like those

Thanks for all that info. Before I make this transfer are they going to be stressed due to the difference in nitrates? Only about 5 in the new tank today, but the old is about 20 since it has been up and going for 2 years. Always had high nitrates and they seem ok with it.

You guys have been great. I get more stressed than the fish when I have to move them!!!!