Your biggest problem with "economy" photo printers is that the business model for printer companies is to sell the printers at close to or even below cost and make up for the profit loss by selling low volume ink cartridges at high profit margins. Sorry, but that's how they do it.
But, for practical purposes, run down to a big box store today (Black Friday) and they may have some good sales: Epson, Canon and HP are brands that have good photo printers at that price. I'd make sure to get one that is designated for photos. Just about anything at that price will print an 8x10 (there are some mini-printers that just spit out 4x6 prints but the letter-size printer is all over the place). If you see cartridges on sale for the printer you choose, grab them because that over time is your biggest expense. The same goes for good quality photo paper.
A 13x19 printer is, as far as I know, out of the question for your price point.