Poultrygirl, I think it's a buyer's market for horses, and making a serious offer of $500-600 is not an insult. If I were your 'seller', assuming they really do want a good home for this mare, I would be very interested in you as a buyer if you told me things about yourself that we've learned here on HF...that you are a responsible horse owner, you're not impulsive, you know what you want and this mare has the potential but isn't quite there yet, you're a college student on a SERIOUS budget, (but future earnings potential for a stable financial future), that you know that the purchase price is just one of the expenses and you will be spending money on vet, board and training...and you'll be riding this girl every day and she'll be well cared for. Those are the types of homes that we dream of for our horses.
If she's insulted by your offer, you can always come up a little bit as long as it's in your budget. I think that the seller should know that she can't get top dollar for a horse that has not been used for 2 years and needs refreshing and getting in physical shape. So, if she's emotional about this horse (and some sellers are, and you have to deal with that) she might not want to come down in her price to meet your offer. She is facing another winter of feed prices and vet bills for this mare, though, which gives you an advantage.
If it's meant to be, it will all work out for you! Keep us posted, and good luck!
PS - have to smile at your comment about "spark of intellect". I bought my 11 year old TWH mare because she met most of my criteria, but she wasn't a gelding, wasn't a bay or chestnut, wasn't a foxtrotter, and wasn't a real pocket-pony people-pleaser type of horse. She also didn't have that obvous spark of intellect...but she has outsmarted me more times than I care to admit! Ha Ha! And, as I've said before, we're having a blast and she's turning out to be the perfect choice, 2 long years of bonding later. Anyway, I am laughing as I say this, so don't take offense - but make sure that spark of intellect isn't bigger than yours!