Here’s what you don’t want to hear: unfortunately, the more you spend, the better the sound. At every step along the way, there’s going to be a mismatch, where one part of your system exposes weaknesses of another part of your system. There’s no way around it. Figure out how much you can afford to spend, without being stressed about the expense, then spend it upgrading your weakest components first, but eventually you’ll need to upgrade your entire system. Look at it like a journey, and enjoy the differences, and the journey, but especially the music.
Of course, during the upgrade process, you'll need to ensure that your components will work together, by checking input sensitivities, and input and output impedances, etc.