1961 Baku repro in Indian rosewood and boxwood for $259 (before current coupon) should allow adding a board for under your budget https://www.houseofstaunton.com/chess-products/circa-1961-baku-wood-chess-pieces-4-4-king. I have no connection to HoS other than shopping there too much lately.
Looking for nice 1950-1970 Soviet Style set

Lots of choices! Every company makes them - something for every budget and every taste:
House of Staunton has a few:
- Ukrainian Grandmaster
- Baku
- Botvinnik Flohr
- Tal
- Odessa
Chess Empire - Shkolnik Soviet
Check out ETSY RetroMaximum and ERWoodLeatherShop
NOJ (but a serious investment…)
https://chessantiques.com/product/sergei-prokofiev-1937-soviet-chessmen/

1950s Soviet Latvian Reproduced Chess Pieces Only Set Weighted Golden Rosewood Christmas Gift - Etsy
Etsy is a great source. Good Luck buying only one, LOL.

This one is not made of rosewood but man its the most beautiful in my collection.
Soviet Latvian Chess Set Reproduction Ukraine Wooden Handmade Chess - Etsy

Lots of choices! Every company makes them - something for every budget and every taste:
House of Staunton has a few:
- Ukrainian Grandmaster
- Baku
- Botvinnik Flohr
- Tal
- Odessa
Chess Empire - Shkolnik Soviet
Check out ETSY RetroMaximum and ERWoodLeatherShop
NOJ (but a serious investment…)
https://chessantiques.com/product/sergei-prokofiev-1937-soviet-chessmen/
Nice list! HoS also offers the GM2 Bronstein (listed as Grandmaster II Bronstein) and GM3 Supreme (listed as Supreme Soviet), as well as the wonderful Soviet Staunton set which originally came out in bakelite and carbolite (presented as Circa 1940 Soviet Club Series).
It should be noted that the Odessa set is a rather crude reproduction of the Sergei Prokofiev 1937 set you mentioned. I find it unfortunate that the reproduction offered by Chess Antiques doesn’t accurately reproduce the insanely long king finials; but in other respects, it’s clearly the better reproduction. I was tempted to get the Odessa set on clearance, but those knights are not my thing at all.
The Chess Empire also offers the Sergei Prokofiev 1937 reproduction, which they strangely list as USSR 1920 Soviet Series. Maybe the design did emerge in the 1920s? I’ve never seen any original of this pattern, so I couldn’t say.
I'm wanting to purchase a nice Soviet Style set (hopefully with board) reproduced from 1950-1970's style. Rosewood and Boxwood. Can I find anything good for around $300 to $400, and where do I look besides the Chess Store?
Thanks, Steve van Osdell