Get any undersink RO system. I went with a tanked system (there is a pressurized tank for storing filtered water) but I have friends who were happy with tankless (tap gives you the trickle of filtered water directly).
I live in an area with very hard tap water (500 ppm TDS); even without a water softener the output becomes ~80 ppm TDS, and the water hardness test strips check out at ~40 ppm. I then installed a water softener with its own sediment pre-filter, and now the overall RO output looks (TDS-wise) even more pure than your typical plastic-bottled water.
I live in an area with very hard tap water (500 ppm TDS); even without a water softener the output becomes ~80 ppm TDS, and the water hardness test strips check out at ~40 ppm. I then installed a water softener with its own sediment pre-filter, and now the overall RO output looks (TDS-wise) even more pure than your typical plastic-bottled water.