Go to a fish store and write down the names of any fish you see you like. It gives a good starting point for people to recommend stocking for your tank.
Once your tank is cycled adding fish is relatively easy. First off don't add too many to begin with. Start with a few fish and then wait a week. Monitor the water quality during this time. If you don't get any ammonia or nitrite spikes go ahead and add a few more a week later. Keep on monitoring and adding until your tank is stocked. This is not quarantining. I highly recommend that you quarantine new additions to a tank to prevent the introduction of disease or parasites. You'd need a second tank, can be a simple one though with a sponge filter, terra cotta pots for decor things like that. And you put new fish in there for two to four weeks to observe them and make sure they are healthy before adding them to your aquarium. Needless to say it takes a lot longer to stock an aquarium this way. It's up to you but I highly recommend quarantining.
For individual fish my preferred method is to use my aquarium bucket. I put the new fish in there in the bag water. I wrap a towel around the bucket to keep it warm and another over it to keep out the light. I add about 1/4 cup of my tank water to the bucket ever ten minutes or so and keep this up until I triple the amount of water in the bucket or more. At that point I net the fish out of the bucket and put them in the tank. Don't pour the water in, you don't want aquarium store water in your tank, dump it out.