Most of the over counter faucets are pretty good. Right now American Standard seems to top the list. Mohen and a few others were the ones to purchase, but as of late, American Standard seems to be making the better product.
Brand however is not really your concern at this point. Because its a rental, you do not want to spend much more the $50 on it. This price range should get you out of the plastic looks like chrome line and offer you a better selection. Pick out something you like, and that your landlord is willing to pay for. After all its not your home your improving its his.
Be sure to pick a brand that the big box store carries in the part isle. Stay away from special sale faucets as this is usually a sign that they are being discontinued.
Check the clearance areas at both Lowes & Depot for something decent at half price. Stay away from price fister....any delta, american standard or moen should perform just fine.
Look into Moen, Delta and Kohler as well trusted brands, check out their pricing in Home depot
We always recommend to our customers to start with Delta - they have a good quality product at a reasonable price. Kohler is good as well but can be a bit more costly. In addition to Home Depot and Lowe's also do a google shopping search and look on amazon - a number of our customers find the faucet that they like and then to some internet research and shopping to find the best price.