Good Morning Ted,
First, I removed my personal offering so as to hopefully negate any bias in my pro stance on the Browning as an ideal first side by side.
The current DGJ has an interesting article on the Browning BSS. If I may quote,
"The Browning BSS boxlock was possibly one of the best field grade side by sides marketed in the U.S. in the last half a century". "Excellent metel to metal and wood to metal fit". "Hand engraved". "Art Issacson, former supervisor of Brownings service and repair facility says The Browning BSS is one of the best boxlock doubles that he has ever seen".
Couple this with modern metalurgy, modern stock dimensions, and a price within reach (by the way, I think your assessment at $1000 is a little low) of the OP's budget and I believe this extremely robust double would make an excellent choice for a first side by side.

No questions regarding the original barrels from my "Frankengun". They were of the 30 inch variety and I had them mated to a Browning BSS Sporter frame, English stock, oil finish, single selective trigger, semi-beavertail forend. Add Briley thin wall chokes and I made my ideal Sporting Clays side by side. Shoots lights out on a Skeet field as well. Absolutely perfect fit.

Respectfully, Bob