What I been doing for years. First thing you always need to know is what do you want to improve, what do you want to make better? If you are real happy with the way things sound now and just want "more of everything" that is very different than if you are unhappy because something is off. Lumpy bass, hyped highs, whatever. These are a different story.
If there is something obvious you can put your finger on then that will be your best shot to cost-effectively upgrade. But if not, then almost always it is much better to leave the components alone and work on making everything perform better.
This is first and foremost tweaking speaker positioning. Next locate the components and route the wires to avoid interference. Simply straightening out a tangle of wires with everything routed to be at least a couple inches apart, never running parallel or in loops, and when they do come close doing it at right angles, these things are free and do improve sound. Get everything up off the floor while you are at it.
Sometimes depending on how bad it was and how good you improve this could be worth a lot.
Next, get every single component up off the floor, rack, etc. Get Nobsound springs, use them under everything. By this point your system sounds a LOT better but you have spent peanuts so if your money is burning a hole in your pocket consider putting the Electrons on Townshend Podiums. Read the reviews and comments, this will be like a whole system upgrade. Better than a lot of components you could buy.
OR another terrific move would be a Raven Blackhawk. Or Nighthawk, more in your budget. Either one, huge improvement! I have the Blackhawk, absolutely terrific amp, not too heavy. Put it on Nobsound, or Pods if you really want to impress yourself.
If you do go Raven, call Dave Thompson and he will recommend tubes specifically for your speakers and taste in music. Seriously, the guy is that good. I am not big into tube rolling, it has been a crapshoot for me over the years. Not so with Dave. The man knows his tubes. Some do cost more but compared to other stuff that is out there his seem a bargain to me.