Good sounding audio typically takes effort. Research and careful choices. However, the good thing is that you have a system to start with. Typically most of us all really start there… then you carefully choose one component to replace after another. If we assume your speakers are adequate, then the place to start is a good solid integrated amp. You want to sell any extra equipment you have and reach as high as possible up the quality level.
There is a couple choices. If you are simply trying to get a really good sounding system then I would look at the highest quality, powerful NAD or Rotel integrated amplifier you can buy… preferably used, so you can be getting a really high quality one. No extra functions, just preamp and amp. If you want tubes, look at PrimaLuna. This replacement should kick the performance of your system way up.
If on the other hand you have aspirations of high end audio system some day, then a used Pass integrated amp (lots of details, punch and musicality) or if you want tubes a Audio Research I-50 is a musical wonder with detail and musicality with natural presentation.
this should kick your system into a really enjoyable place and give you the basis for additional improvements as is convenient for your finances.
All of these brands are highly regarded and reviewed… so you can read multiple reviews on them and start becoming acquainted with the literature on audio. Stick with Stereophile, The Absolute Sound and HiFi+ for reviews. These are the most reputable and neutral.