Cygolite Hotshot Pro 80 rear red LED -- easily the brightest I've seen locally in the $50 and under price range. It's the only light I've seen personally in that price range that's bright enough to be effective in daylight. It's actually too bright for nighttime use on the highest output.

In a front light, I like the Serfas SL-255 (around $30 or so on Amazon), which uses a pair of AA batteries. Usually I run NiMH rechargeables, but I like being able to grab a pair of alkalines from any store if necessary during a long ride away from home. It's rated at 255 lumens on the brightest steady and flashing modes. Bright enough to be visible in daylight, but not enough to blind anyone. I checked it myself in daylight and night by eye and video cameras. In traffic in daylight I aim it straight ahead -- it's not bright enough to blind anyone in daylight. On the MUP I aim it downward, mostly on the front wheel. At night I adjust it up and down as needed while riding. Depends on the road, ambient light from street lights, and type of road. On two lane roads I'll aim it more downward. On wide boulevards with multiple lanes on each side, I'll tilt the light upward a bit more to light the road ahead and be seen more readily. It's nowhere near as bright as most car headlights so drivers have no reason to be distracted.