I'm not sure what the base system is like. I know that just simply replacing my front speakers in my shaker500 did the trick for me. I know it's not perfect, but for $60 I got a definite improvement in sound. The OEM speakers are very cheap.
I don't think you can use the word "audiophile" and budget together. I would set a price on how much you want to spend, decide if you're going to do it yourself and where you'll get the parts from. I would personally go to a few car audio shops and get their recommendations. That way, even if you don't use them for the work, you'll have a pretty good idea of what they would do. Additionally, if you're particular to a certain brand, make sure you call around. Audio shops tend to push a few brands, and won't carry others. I called one shop and he kept pushing Focals on me because that's what he carried. I kept asking for other options and he continued to insist that was what I needed. Funny thing was, I called four other guys and they all recommended other brands lol.
Since you have the base system, I would probably invest in a better, cleaner amp. I would say the shaker amp is boarderline, so I would think the base amp sucks even more.