Depending on how soon you want to make the purchase, you might wait to find a used VPI Scout with JMW 9 arm. This is a new model that VPI recently introduced for $1500 for the turntable and arm combo, so it should sell $1000 or less on the used market. The other VPI option is the HW-19 Mk III (used) or the HW-19 Junior. Both of these HW-19 models offer an upgrade route to the HW-19 Mk4, which is an excellent turntable. If the used turntable does not include a tonearm, then the Rega RB300 or RB600 would be a fine combo.
The obvious other choices include the Rega models in your price bracket, the Music Hall MMF-7 or MMF-5, and the Pro-Ject turntables (the same factory in Czechoslovakia makes the Music Hall and Pro-Ject tt's).