These don't come up for sale too often - shame about the stains on the dial, but rather valuable regardless.
An eBay ad with clear pictures from all angles, taken in indirect daylight would be your easiest way to get market value for it. It might sound odd, but I think the picture quality a modern iPhone can produce will be enough, and here's why:
The dial is in a pretty rough state it seems, at the bear minimum there's significant stains on the polished, outter part of the dial between 8 and 10. This alone means it's not attractive to a hardcore collector and reduces the value significantly. It is still a solid gold watch with a solid gold dial, though, so the price won't be effected as badly as it would be on a stainless steel watch, for example. A very good example might fetch something like 3.5-4k$, for this one it might only be 2.5k$+ - still a lot of money, though. To get to the high end of the price range, many detailed pictures are necessary to show the watch is actually in great condition. For yours, standard, good phone shots from all angles will suffice in my opinion.
Now, to the bracelet. I have to admit that I'm actually looking for a yellow gold 7077, which is what yours is (even though it might not say so anywhere on it), so from my own research from the last year or so:
A full length example weighs 57g. To check yours for full length, here's one for comparison. Excuse the bad lighting, I hope it'll still serve the purpose:
Red are the endlinks that sit between the lugs of your watch. Don't count them in. Yellow are the "regular" links - it should be 8 on each side. Green are the "double stretch links". On mine, you can see 3 double-links on each side of the clasp, note that the factory length that brings it to 57g would be five in total (2 on one, 3 on the other side). I can see 5 in one of your pictures, so for now I'll assume yours is full length and thus weighs 57g. For your own count: it's easiest to just look at the outter row.
Since it's on an 18k watch (the so-called "deluxe" Constellations with solid-gold dial don't exist in 14k), I assume the bracelet is 18k, too. At current gold value, that'll bring it to roughly 2250$. For one of those "flatlink" bracelets in very nice shape, you can add ~30% in value, so approx. 2900-3000$. Yours will likely be a little less, the center pieces look like they don't carry their original brushing anymore and it's a question if the stretch links (marked green in the pic above) do actually still stretch smoothly or if they need new springs etc, but all that won't bring the value down by much. I don't see this go for less than gold value + 20%, which is still 2700$.
While, personally, I'd love to see you split bracelet and watch in separate eBay auctions, as I'd surely be bidding on the bracelet, I think I'd honestly rather keep them together if I were you. It's a beautiful combination and might draw in more bidders. Either way, it's certainly not going to make a huge difference. Expect to get 5k$ or a bit more in total, minus eBay fees. That'll be significantly more than pure gold value, which should be very roughly 3600$ or so.
I'm glad it's worth more - melting it would be blasphemy, frankly.
😀