A good audio playback system is made up of many components. What good table radios do, if they exist, is combine all of the components into one spot. Radio receiver, amplifier, speakers are all bundled into one nice, neat little package. Building a good home audio playback system is tricky because you need to mix and match separate components. Your 1050 is a great place to start for good sound. I have owned one for over 5 years and have been very pleased with its sound quality. I think believing that an "upgrade" to NAD or Arcam is going to make that noticeable difference is a little silly as their sound is very comparable to the sound that your 1050 can produce.
Where you can help your 1050 out is by upgrading your source components and also possibly your speakers. What do you use as your source when you play CD's at home? Do you use your DVD player or a dedicated CD player? You may not believe this, but a dedicated CD player will produce a better sound than most entry-level DVD players even when connected in the exact same method. I made this switch with my system from a Sony DVD player to a dedicated CD player and the difference was very noticeable and all good.
Your speakers, while being a good buy for entry-level speakers, are not really helping you at this point. You said it yourself, their fine on movies and video games, but not on music. This is a very typical response to entry-level speakers. The ERA brand, though I've never heard them in person, seems to be a good speaker to upgrade to. I would also suggest looking for a store that sells Paradigm or PSB or NHT or B&W brand speakers and taking your favorite CDs and listening to them. If you're more inclined to shop online, take a listen to Ascend Acoustics, or the Onix brand over at av123.com or even Outlaw's own speakers. Every single one of the brands I mentioned will give you a pair of speakers that will give you a better sound than your Insignia's.
Only your ears will tell you what type of sound you like. Take a favorite CD to a store and listen. Or, order a pair of speakers online and try them in your own system. What sounds "bright" to someone else may sound perfect to you.
Though the following article talks about a particular speaker brand, it can apply to all speakers:
http://www.audioholics.com/education/loudspeaker-basics/how-to-judge-loudspeakers-sound-and-accuracy Good luck and let us know how it works out.