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 have an APEC systems RO-90 in my parents home and an APEC RO-hi system in my house. They work fantastic and are easy to install. Brings me peace of mind knowing my drinking water is super clean

Get a 5-stage RO system without a tank. Tanked systems are only a good idea if you use enough water that the tank doesn't sit stagnant and you include UV, otherwise tanks can be a place that causes bacterial growth. The reason you want a system with more stages is that you can have multiple pre-filters before the RO membrane which allows the membrane to last longer and allows cheaper filters to be the most often replaced.

There is a user on this site that commented recently on installing one. The problem is I can't remember what thread it was or what his username is, or even what the name brand of the system he installed was.

I use an APEC 3-stage filter system. Works well. APEC seems popular and widely availablele.