One of the roles of a turntable is to provide a good platform. Turntables are much better if they are on a stable platform. A Solid Steel 3 will give you a very solid platform; a 3 shelf unit is $700, and a 4 shelf unit is $900. If you buy a 3 shelf unit now, you can buy a kit to add one or two more shelves in the future. I have a Mapleshade Samson rack, which is even more stable, but that would be outside your budget
The Rega P3-24 that Jim Bennet mentioned would be a significant upgrade over your TT. Rega tonearms are very good for the money. I have had friends who purchased Rega's, and they found that it was overly sensitive unless it was on a very stable platform so see if you can test it out at home before purchasing it.