Choosing the TT will be fine, for your budget there will be many options.
Going for vintage will most likely require additional monies are required to be spent, as a service will be required, and if done by a skilled individual advisories might be supplied, suggesting other parts are exchanged.
The first Cart' or even second Cart', need not be too costly, these are very fragile, and a incident is always lurking where the Cart' is the part that comes out the worst. On this type of experience having been met, you are not alone.
One other thing to consider as ownership and usage evolves, and one that can really benefit a TT, is considerations for how it is mounted. A Equipment Stand/Rack, Wall Shelf, or dedicated Table. All will benefit from having a Sub Plinth and Footers used to support the TT. The learning of how differing configurations influence the sonic being produced, is not needing to be expensive. The results that can be attained will really impress.