I would be partial to a 1970 Brown Stained French Lardy set with a 4 1/4 King as well as a vintage gold patina Drueke chess board. 
You have $600 to spend...
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Depends how you want to allocate the money (e.g., you could spent $580 on a set and $20 on a silicone or mousepad board). As generic advice on $600, if you want both wooden board and pieces, I would say you can probably do a JLP board and a mid-range HoS set; if you want to go Bobby Fischer style with silicone/mousepad and wooden pieces, I'd say go with a Noj Dubro and a silicone or mousepad board.
I bought my chess set for $50 (Polish production).
$600.. I think it's too expensive...
Buy
All the advices people posted above are good. But if you're unsure about which chess pieces to get, just get an inexpensive Staunton styled pieces with a 3.75" sized King. You can't go wrong with that. Then with rest of your money, spend it on a high-end wooden chess board.
Here's a nice tournament-sized end grain board from MTM Wood with 2.25" squares that costs $538.50:
https://mtmwood.com/en/chessboards.php?product_id=4384
And for the pieces, there's a nice Reykjavik 3.75" from Chess Bazaar that costs $59:
https://www.chessbazaar.com/the-reykjavik-staunton-series-weighted-chess-pieces-in-sheesham-box-wood-3-7-king.html
Reykjavik is styled after the famous set used at the 1972 Spassky - Fischer World Championship Match held in Reykjavik, Iceland. There are, of course, other less expensive options for the pieces, so surf & compare.
The reason why I'm recommending you to spend most of your money on a board is rather simple: it's because you're posting to this forum :-)
Anyone who frequents this forum more than likely end up having more than a single set of chessmen. You might as well start off by getting the best board for your home while you have the money, because no matter which nice chessmen you get, there's always another one you will lust after (and order).
Save more money and buy a new phone.
You can play chess on your screen.
I’d spend ~$30 on a vinyl chessboard and Marshall analysis set, $570 on books.
What about using some of that to get some books and learn? Or lessons?
$600 ??....im going to St Thomas for da weekend.
sound advice, sound. 😎
Oct 15, 2020
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#12
I agree that it depends on what you value more and what style of pieces and board you prefer.
I also believe in paying attention to what you say. So, a wood set includes both wood pieces and board. Of course there also is the option of having wood pieces and a nice mousepad, thin, board like the FlexPad board from The Chess House.
With either the pieces or board you will need to decide on what color of wood you want.
If I were going to buy only one nice wood set it would be The Craftsman Series set designed by Frank Camaratta. It is sold by The House of Staunton. I personally have this set in the Blood Rosewood. This is my favorite Staunton styled set.
For the board, I would look at the Colorado Woodworker ones on Etsy. I would also talk with the guys at The Chess House as their wood boards are really nice. And I would buy a FlexPad board from them as well. Their FlexPad boards are arguably the best of the thin mousepad boards available, and they’re inexpensive.
Of course, this is my opinion and tastes.
@MCH818 and @eyechess Part of the idea in this thread is to get some idea what is available and to learn what prefs it is best to express, so some additional notes based on what you set:
I am indeed looking for a set, so pieces and board, and was thinking wood for both but am now reconsidering. The best pieces I have now are House of Staunton Zagreb '59 in Golden Rosewood and Natural Boxwood (3.875" king)...but it is interesting/odd because my ex-wife purchased it direct from HoS many years ago, and it says Zagreb 59 on the box, but the king has a cross rather than point that I see in pics of their current set. I have it paired with a folding HoS Palisander and Maple Board with 2.25" squares.
That said, I do have an HoS Maple and Mahogany tournament board with 2.5" squares, so for the right set with dimensions to go with that board, I could splurge on the pieces and a flexpad board or the like. Though based on some comments above, I'm now wondering if I shouldn't do the opposite and secure a really nice board first
I am mostly interested in Staunton or Zagreb (is that the best name for them?) style pieces. I'm not too fond of the style in #5 above and have no interest right now in really out there modernist pieces and the like. There might be styles of pieces I don't even know about.
No real preferences on color. I don't have any wodden pieces that are ebony/ebonized or even dark in any shade such as blackwood or blood rosewood, etc.
At any rate, I know this is a bit vague but I am really benefiting from the answers to the question that you can interpret as you would, which is: if you had $600 to spend on pieces and a board, what would *you* choose based on your own preferences, expanded to say: wooden pieces and any kind of board
Thee_Ghostess_Lola wrote:
$600 ??....im going to St Thomas for da weekend.
I hear you, but this is a birthday splurge during Covid times
passedpawn22 wrote:
I’d spend ~$30 on a vinyl chessboard and Marshall analysis set, $570 on books.
Oh, I've done that. Multiple times 
Oct 15, 2020
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#16
Well, I would get the Craftsman reproduction from Frank Camaratta directly at chess antiques.com. He has the set listed at $295 while HoS is at $349 for the same set.
Then I would buy a 4 piece, magnetic wood board from Colorado Woodworker on Etsy. For the woods I would get American Walnut and Maple.
I would also buy a FlexPad board in the standard green from The Chess House.
All this will keep you within your budget as well.
@Eyechess - The Craftsman repro looks beautiful. From the descriptions on chessantiques, they appear to be repro of Golden Castle Craftsman, which in turn was a repro of Jaques Marshall set. Another beautiful repro of the Marshall set is the original 1966 Havana and I think Frank Camaratta did a wonderful job with their repro. I would like to acquire one some day.
Oct 15, 2020
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#18
zagryan wrote:
@Eyechess - The Craftsman repro looks beautiful. From the descriptions on chessantiques, they appear to be repro of Golden Castle Craftsman, which in turn was a repro of Jaques Marshall set. Another beautiful repro of the Marshall set is the original 1966 Havana and I think Frank Camaratta did a wonderful job with their repro. I would like to acquire one some day.
Yes, Frank has had a number of reproductions made that are excellent. I argue these newer sets are likely made better than the originals.
Oct 15, 2020
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#19
Board: A nice Drueke style classic board in walnut and mahogany 2.25". You can get it from JLP, ChessUSA or Etsy seller Colorado woodworker. ~$300 from JLP and ChessUSA less from Colorado woodworker.
Pieces: Options from House of Staunton Craftsmen 3.75" or Cooke Series Luxury Series 3.625" or Camerata Collection 1849 4"
Staunton Castle: Their 1950 Dubrovnik 3.75"
I am confident that any person who goes over to your home would be very pleased to play on had board with any of those sets.
I'd like to get a nice wood chess set for home use. Coordinates or not, folding or not, etc., are all on the table. I've budgeted $600 for board and pieces. What would you get?