Good spectrometers in "new, unopened" condition are out of your budget. Their prices start at about 2000 USD. This also includes the spectrometers specifically made for education—like the ones from PASCO (example; they are usually based on Ocean Optics components), and from Ocean Optics themselves (example).
One option for your budget is to buy a used spectrometer like Ocean Optics USB2000. There's quite a number of options on Ebay, including one for 700 USD (example; the link will likely rot soon), and some more on Amazon (example). But note: you should make sure you ask the seller about wavelength range and resolution, as Ocean Optics spectrometers of the same model can be configured with different slits, gratings, detectors and filters.
These are the commercial solutions, with a quality reflection-based diffraction grating, focusing mirrors and a CCD detector. Here's the typical optical bench of an Ocean Optics spectrometer (image source; the rubbed pale-reddish line on the left-hand side is the place where the CCD detector is to be placed):
Another option is to get something from Thunder Optics. I have tried "Mini USB spectrometer", which currently costs about 100 USD. But this one not only has much smaller price than the Ocean Optics spectrometers—inside it's basically a DIY spectrometer: a cheap wobbly transmission grating (secured in a plastic holder to avoid too much wobble), a web camera as the detector, and a fixed thick slit in the thick (1.5 mm) aluminium case. The components are fixed in place with some kind of black glue.
This kind of spectrometer isn't useful for anything but a qualitative* look at relatively bright** sources of light.
Here are two photos of my item ("optical bench" and the slit):
* Qualitative, because you can't get raw data from the camera.
** Bright, because the camera has quite low sensitivity, and the optical bench lacking any focusing mirrors reduces light gathering capability.