I know the markup on diamonds and jewelry is quite extreme in terms of profit margins. . . .
I am planning to ask my girlfriend of 12 years to marry me and I would like to get her a nice ring without totally being taken to the cleaners. . . .
I should mention that I am fine with a lab grown diamond as well.
There are diamond/jewelry wholesale districts in every major city. You can often get good deals at a jewelry mart if you know what you are looking for. Take someone with you who knows diamonds and the current market if you don't have that knowledge yourself. You can usually pick a stone and have it set into the ring of your choice rather than be limited to pre-made rings.
You may be fine with a lab grown diamond, but get a natural diamond if at all possible. Your intended may not rush down to the jeweler to have her engagement diamond appraised for insurance, but sooner or later that is going to happen and that's when the issues usually arise. Don't believe her when she says a grown diamond or cubic zirconium is just fine. Those are well intended words, but women really do care although sometimes that caring doesn't manifest for many years. [And don't misrepresent to her what the stone actually is if you do decide on a man made or farmed diamond. That would be a seriously bad move.]
Don't settle for lesser grades, but you don't need the highest grade either.
Don't buy a ring or loose stone at the mall. You will pay top price.
Pawn shops are a source for diamonds, but I wouldn't try to use a setting from the pawn shop. No bride wants a used ring unless it is actually a family heirloom or the pawned ring can be traced to royalty or someone famous. I would have a stone acquired at a pawn shop put in a new or custom setting. As with the jewelry mart, you need to know what you are buying without placing your trust in the sales person. Take someone with you who knows what they are doing if you don't have that knowledge.
If you have to stick to a tight and firm budget, put your money into the stone and get a simple solitaire setting. You can have good stone set in a spectacular setting for a special anniversary during your years together, but a cheap stone will always be a cheap stone.
FYI - It has been a general rule of thumb in the U.S. for many generations that a prospective groom should spend approximately two months gross salary for an engagement ring. If you make the U.S. median wage of $62K, that's about $10,000 for the ring, not $800-$3000. Even at the U.S. poverty line of $12,880/year for a single person 2x monthly earnings would be $2,200. [Please don't shoot the messenger.]