For example, a Gold Sovereign from the early 1900's being sold for melt is nothing special, right? I should be able to find people here with the same deal, or a local coin shop/pawn shop, etc.?
Pretty much, but it depends on supply/demand. At times I have seen slight premiums. I buy this stuff as a dealer of mine has it, but he can go quite a while without any on hand.
If you are talking roosters, German 10 marks, or something similar, then yes, you should be able to get them for just about melt (there is going to be a small premium, but not much). Apmex has them, you can find them on ebay, they are available.
While I agree with this, in my experience if you make contact with local dealers you can do better, but have to wait until something comes in. At spot, I have got every 20th century Mexican gold coin, all French after Napolean I, and even scarcer pieces in higher grade at times. If you want to rush, the best you can do is what PF suggests and get the most common items for close to melt from more retail outlets.
Are you buying them as a substitute for bullion or for your collection? If as bullion, I would buy actual bullion coins which are a lot more liquid. in my opinion it is a lot easier to buy common world gold than it is to sell it.