You will certainly get an improvement with a separate phono stage.
I own the Herron VTPH-2A, which is out of your price range.
Of the stages I've personally heard, I can recommend a short list of new products.
Musical Surroundings Nova III
Parasound JC 3 Jr
Sutherland Insight
All are very good sounding preamps with options for virtually any cartridge you might want in the future.
There are undoubtedly many others in this range, plus many more if you are willing to go pre-owned.
At this price point, I would personally stay away from tube stages, unless I were willing to buy on the pre-owned market. That doesn't mean you should.
I own the Herron VTPH-2A, which is out of your price range.
Of the stages I've personally heard, I can recommend a short list of new products.
Musical Surroundings Nova III
Parasound JC 3 Jr
Sutherland Insight
All are very good sounding preamps with options for virtually any cartridge you might want in the future.
There are undoubtedly many others in this range, plus many more if you are willing to go pre-owned.
At this price point, I would personally stay away from tube stages, unless I were willing to buy on the pre-owned market. That doesn't mean you should.