I have read more and more and my vision on what may be best for me has changed.
I probably have a mercury poison problem and I have started a trial chelation (frequent dose chelation).
I hardly can find any success story of ionizers, so I think I will not buy one soon. As most people who chelate are using either R/O or distilled, I am reading more about that. See for example:
To alkalize I am drinking lots of vegetable juices and wheat grass. With that my morning urine pH has raised significantly (from 6.1 to around 8) without using an ionizer.
I am just about to test my tap water for metals (via http://www.doctorsdata.com).
If the metals appear to be high, I will probably go for distilled and add some alkalizing minerals if I think that is necessary (of just a little bit of Sea Salt and epsom salt).