I suggest going out to some hifi shops and listening to different gear, especially some very high end gear, to get an idea of what is possible and then make plans to build your system towards a reasonable (affordable) goal.
Several hints:
-Source is very important - garbage in, garbage out. look for a nice CD player, DAC/computer server, or turntable as the basis for your sound system.
-Deep bass is hard to reproduce with any fidelity, and you either need to buy very large floor standing speakers with a very poweful amp to drive them, or add a good subwoofer to augment your speaker/amp combination. Subwoofers usually always comes with issues of matching as you are now adding and tuning another crossover yourself - best to have a sound meter and test disk at least. Quality bookshelf speakers on good stands or small towers with decent amplification can reproduce low enough bass to provide convincing replay of acoustic jazz, vocal or chamber music without augmentation. Orchestral music, hip hop or heavy metal usually require more oomph.
-Don't ignore wires. The rule that many people start with is that wires should be 10 to 15% of your system cost. I feel that for budget systems this number should be more like 15 to 20% or more, although if you shop carefully, there are deals out there to be had. And yes, an after market power cord does make a difference, even (or especially) with budget gear where smaller transformers are used to cut costs. I would upgrade wires in this order - power cord, interconnects, speaker cables.
-Physical set up of your system and room are critical and the most important element of good sound, espcially in your case with the hard surfaces. Whole books have been written about this subject, but a few hints here. Adjust speaker distance from the back wall and adjust separation and toe in to dial in the best stereo image and balance of treble and bass to other parts of the sound spectrum. Isolate your equipment, especially CD players and turntables from room vibrations and make sure your speakers have a solid connection to the floor through quality stands and/or spikes. There is a lot of information available about this online.
-Don't be afraid to buy used gear, you can typically get one dollar of performance for every 50 cents invested compared to buying new once you know what to look for.
One of the better descriptions (in my opinion) of how to evaluate the performance of any stereo system can be found
here.
Good luck in your Quest.