Upgrading to a stand alone DAC

In terms of your budget, I would second the suggestions for looking at Schiitt DACs.  I have a Gungnir multibit that I like quite a bit. I also have a Mytek Liberty II and I've enjoyed that but the top end has to be tamed a little bit, so depends on system synergy. I also personally don't love the user interface on the Liberty, but I do like its being fully featured with a top of the line chip. 

If they make any difference at all, IMHO digital cables and similar tweaks would be quite secondary in terms of priority - get a well constructed DAC first and then see if you need to worry about that stuff with a later separate budget. 

And I agree that speakers can make the biggest change in a system, and even adjusting their toe-in can have a huge impact. 

@helomech  +1

Many of these  DACs have very inexpensive IC chips costing less then $1. Cost restraint prevents them from using discreet op/amps.

An inexpensive "Chi-Fi" DAC can be had for as little as $300 with an interchangeable op/amp chip option (Aune X8 with balanced outputs) and then for an additional $100 add a Sparkos ss2590 DISCREET op amp runs in Class A.  For a total of around $400 it's unbelievably good. 

or

(For twice the price) Geshelli socketed J2S and add the Sparkos or Burson Vivid discreet op amp.

I wouldn't be surprised to see Schiit  come out with a socket replaceable DAC op/amp feature in the near future.

Up grades can be had by simply plugging in a new chip instead of buying a whole new DAC.

The money you saved could then go into better speakers yielding a far higher performance level. Heck, maybe you won't even need new speakers!

I’d like to second the Bifrost 2 recommendation.  I went from using my NAD C568 CD player to the Bifrost, which I later upgraded to the Bifrost 2/64.  I could definitely tell a difference moving from the internal DAC in the CD player to a a stand-alone DAC.  The upgrade to the 2.64 added a modest improvement.  I can only imagine that the Yggy by Schiit would be yet another step up.

Would I hear a significant difference at this price point?

Difference in DACs can be huge or very subtle, depending on how resolving the rest of your system (and room) is. 

Chord Qutest is an amazing DAC. Get one used around $1,000 and flip it if you don’t like it. I owned it and several DACs later still hold it in high regard. 
Another good choice is a used Benchmark DAC 3 - slightly more detailed than the Qutest but more analytical/sterile sounding. PS Audio DSD DAC is excellent as well. You can score one in your price range. Smoother more analog sounding but very musical with excellent detail retrieval. 
Stick with a major brand DAC and you should be fine  

Good luck in your search. 

Would I hear a significant difference at this price point?

Aged and untrained ears are not going to hear significant differences.

But, the slightest difference can become quite significant for someone over time and dominate their psyche (most audiophiles might fall in that category).

If your budget is restricted to 1500, the Gustard R26 (the R2R version) is an incredible dac that often goes on sale for right under 1500 dollars...You could rip all your CDs, put them on a NAS and it will stream those files from your NAS, without the need for some extra streamer and cable botching things. Most stand alone dacs won’t offer you that capability..... Err...awful name though i know (rhymes with some bastard munching on custard), but if you can get past the brand name, it’s a good dac.