Base trims: 175/65-14
LE/S trims: 185/65-14
Myself, I'm running the larger 195/60-14 tires - little meatier in the tread, but keeps the overall circumference close to stock size, so the speedometer reads correctly. Can be hard to find - selection of 14" tires vary from the manufacturers from year to year. The 8th gen Corolla can take wheel offsets from 38-45mm, no wider than 205mm tread (7" wheel), without potentially running into a clearance issue.
Like dom mentioned, there is no universally "best" tire for everyone - depends on what you want/expect from the tires.
Some are optimized for wet/dry performance - some are three-season tires (can handle snow, but not as well as a dedicated snow tire). Compounds can be optimized for maximum traction and heat dissipation or long tread life, smooth/quiet ride.
Example - I'm running Borbet alloy wheels (14" x 7" @ 12lbs) on Bridgestone Potenza RE960AS Pole Position tires (195/60-14). Personally, I'd trade a little tire life/comfort for more traction/better temperature stability - as I run more highway miles than city miles. I typically get about 40-50K out of a tire, Try not to run them more than 1/2 worn - still legal trad depth, but the traction benefits and hydroplane resistance drops quickly once you wear them more than 1/2 way down.
Funny you mention the 16" wheels - I was the same way. ran 16x7 wheels on 205/45-16 tires. Love the way they looked, especially with a drop - but was tired of have to avoid every single pothole in the DC Metro area (soemtimes impossible to miss). After bended some of my wheels on two separate sets of wheels (one low pressure cast, one forged!) - I punted and got some lightweight 14" alloys. The car is pretty much unstoppable on rough roads, shrugs off the occasional pothole. Plus - I don't feel a significant loss in handling, still can drive as I want to - ie, still takes corners well, good stability, good steering and braking feedback.