Which fish to start with?

I have limited experience so I can't really offer too much informed opinion on fish choices. I would, however, suggest that you either get some media (filter floss, gravel) from an established tank to seed your tank with bactieria or get Bio-Spira if you're going the fishy cycle route.

I started my fishy cycle and ran it for a week before I got some filter material from one of my lfs's tanks. That jump started the cycle but I still wasn't happy with my fish dealing with the stress of a cycle. I got Bio-Spira after week two of cycling and the tank was cycled two days later.

My next tank will be cycled with Bio-Spira from the start. Its the best of both worlds to me because the fish aren't exposed to much stress and you don't have to stare at an empty tank for weeks.

If you don't do fishless cycling, prepare yourself for daily testing and frequent water changes. One of the problems with cycling is that each addition of fish results in a spike, so you have to be careful when adding sensitive fish. And, since many hardy fish are territorial, they can not go in first, even though they would survive, since they will claim the entire tank as their own, and beat up any newcomers.

From that list, the danios are probably the best first choice. They are hardy, and not territorial.

Tetras are a good second addition, but should be done in small batches to avoid high spikes. Go with a larger adult size--neons are a food source for angels in the wild, and may become snacks once the angels are adult sized.
The other cichlids will be territorial, as are barbs.

Cories will eat angel eggs, so if you're interested in breeding, they should be avoided.

Gouramies will squabble with the angels for the same areas of the tank, and may result in injuries and fin damage.

Clown loaches would be okay, though they will all get large, prefer groups of 3+, and shouldn't be added first--cycling will stress them and they are prone to ick.

Avoid painted glass fish--the fish is treated with dye, will not stay that color, and tend to be prone to diseases. Glass fish also tend to prefer slightly brackish/hard water--not good for angels.

Many of the fish listed are not really appropriate--some prefer much different water conditions (including a few species that are brackish). At least one of the knifefish mentioned gets to an average of 2-3 foot in length--much bigger than your tank can support. Ditto for irridescent sharks--huge fish, not good for the aquarium.

I would look at the fish, see what you like, then research them individually. That list is hazardous, IMO, due to the variety of water conditions of the fish listed, some outright incompatibilities, some innapropriate for aquarium fish, etc.

I know you say that you are not comforatble putting pure ammonia into your tank but don't forget that the fish create pure ammonia, so it is getting in there one way or the other.

Bio-Spira is a great alternative as it will instantly cycle your tank. But stay away from other bacteria in a bottle products as no others have been proven to work. Bio-Spira has to be kept in the fridge so it stays fesh.

Keep in mind that you won't see huge changes. 5 small fish in 65 gallons won't create a huge spike, where the same 5 fish in a 10 gallon tank will make it toxic in short order. Nitrites don't usually show up until the 3rd or 4th week, so I would wait at least that long before adding more fish.

Wow--someone who actually is patient! Heck, that's the biggest thing most fish keepers lack--you'll be fine!