You have experienced a high quality system in a controlled environment. You may not be able to duplicate it exactly in your room but you can vastly improve your room experience and over time, as your budget allows, you can improve it.
Since you say your music consumption comes in the form of digital files on your Iphone you need to start educating yourself as to what kind of files ( think of file formats as containers ) you have and what kind you should be acquiring moving forward.
Many Audio Music Files such as MP3 take the music and compress so it will be smaller. This results in a loss of data. While this may be good for reducing the amount of storage space you need to keep all of your music it is not good for preserving the best quality of the music you love. I do not purchase much digital content ( i buy vinyl albums ) but when i do i make sure i am getting the best/largest file available.
If you only have an iPhone consider getting a media storage hard drive for your room because if you love music you will be maxing out your phones capacity at some point.
Next is your playback equipment. If you play those nice big files on a low end receiver you will not be getting full potential of your nice big files. Rather then getting a better receiver first you should invest in a DAC ( Digital-to-analog converter ) You do not need a super expensive one but you do need a step or two above the low end ones. You send the music from your phone into the DAC and then from the DAC into the AUX inputs on your receiver.
Your Polk speakers are probably semi decent even if they are low end, but they probably lack good bass reproduction. You will want to upgrade in the future but I would say your next investment would be a good sub-woofer. I do not know what outputs you have on your Sony but if you do not have a sub out jack and you do have the ability to out put to two sets of speakers A and B you could use the B outputs to send a signal to the sub through its high level inputs. This YouTube video will explain it.
Having a sub-woofer will dramatically improve your listening experience.
Now you will have improved your music reproduction you need to improve the space in which you play/listen to your music. Sound waves can bounce around and off of walls and ceilings and have bare walls will sound like you are getting a echo-y boxy sound. There are a lot of factors to this and will not get into it here but just say it is important, speaker and sub-woofer placement is also important.
Which brings us to the next thing you should get, KNOWLEDGE. ( which is actually the first thing you should get )
Research, study and learn as much as you can. There are great forums out there for reading and asking questions. Two good ones are Stereophile.com and audiokarma.org
With that knowledge you will then be able to wisely start upgrading your equipment.
Since i am a vinyl lover i have to say buy a turntable and get an album of an artist that you have digital files of and listen to both and you will feel the soul in the vinyl version that may not be present in the digital file. If your receiver does not have Phone inputs you will need a phono-stage or pre-amp before you can use your turntable, remember what i said about knowledge. There is great digital music out there but there is an ethereal or undefinable quality to vinyl that is so pleasing and satisfying.