I haven't tried them personally, but I'd take a look at either a "Doff" or a "Balalaiker" brand balalaikas. They're made in Russia, made new and are within your price range.

For example

See here for a Doff

https://www.amazon.com/Professional-balalaika-extra-strings-Handcrafted/dp/B07NGK3QDL/

And here for Balalaiker

https://www.amazon.com/Balalaika-academic-student-Balalaiker-Resonant/dp/B07N6MV25D/