Ok .. sounds good so far.
Adding live plants ... if it's in your future plans ... could help with stocking.
But first thing's first. I'd say once your cycled, you could look to add one more red-eye tetra and maybe two more neons to increase your current schools.
Unfortunately in a 60liter your limited by what you can comfortably fit. If your looking to add a different schooling fish, you could look at cardinal tetras (though they look like neons) or some Rasboras. Also, consider inverts like ghost shrimp. They stay small and have almost no bio-load.
My son has a 10 gal with 3 Neons, 2 Cardinals, 1 male Albino TigerBarb (rehomed from my DT .. was getting bullied) and at least 3 Ghost shrimp. So far so good ... but I also have some plants and Driftwood to help with nitrates and surface area for BB. I have the old school bubbler with Polyfill and Carbon (came with the 10gal kit) so I don't have a heavy duty filter.
Still .. keeping the fish you want in a 15 gal is possible with your set-up.