You can get plenty of bikes for around 4k, especially if you dont care about the looks. A 250 can be had for 2.5k in good shape, and a 500 for around 3. Look into the SV's you should be able to find a 00-02 for around 4k, and there are always some pre-rashed F4i's.
While I recommend getting a cheap bike, dont skimp on the gear. Not only does your health depend on it, but you will also have it on all the damn time. Its better if its comfortable