I'd seriously keep my eye pealed on pcpartpicker for a card in the 100 dollar range its really hard to find a card worth recommending at that range. I would say if you can spend the extra 20 or so dollars on a 650Ti. It is a better card then the 7770 however if you are pushed for cash then a 7770 will just just as well just the same.
I don't have a preference on brand and I'm not an Nvidia or AMD fanboy. I borrowed my friends 7770 while he was in the process of building his rig, performance seemed great for what he paid for it ($130). However, on Newegg there's some refurbished cards such as a GTX 460 and an HD 6850 for around $100. Wouldn't one of those be better than a 7770?
I wouldn't honestly. I wouldn't purchase a card from a previous generation I feel you get better exposure to newer technologies. More power efficient cards which may not show on the bill when you buy the card but they will on the power bill. Tech such as shaders, DX11 support and how well it performs on the newer gen cards. I would get a brand new card if all possible. You never know what happens when a component is returned to the manufacture and sent back for resale or replacement.