By mechanical removal, I do not mean some machine with has tiny tweezers to remove things out of the water, I mean filtration. Filtration can be the least expensive and most often needed type of filtration and is the only thing I would recommend even if you have no need.
A simple filter, with replaceable filter, can be used to remove particles from the water. This means sand, dirt, particulate iron and not do often particulate manganese. This is put in an accessible location and changed as needed. You can use it on water company water to remove the particles, when they clean the pipes.
These simple filters will NOT REMOVE lead, copper, radon, salt, chlorine, bacteria or hardness.
After the simple filters, you get into filters that have "micron" ratings. The most common is a .5 micron and that will remove a lot of items, but I have to keep in mind that when I test for coliform bacteria, I use a .45 micron filter to "catch" the bacteria so I can enumerate them. ).5 is bigger than 0.45 and will not catch as much and if I want to catch all the bacteria (or most of it), I would use a 0.2 micron filter (still smaller). So be careful of hype, 99 % removal is not enough!
Some carbon filters are also used and rate as particle filters and have an added benefit of taking out chlorine and nasty organic contaminants. You will see carbon filters rated for removing lead and they will remove some, but most lead is dissolved, not particulate and the get it out you really either need to redo the plumbing or get the next level of filter.
The next level of filter is a reverse osmosis and it basically lets water molecules pass and not much else. The main issue is that home versions only produce about 5 gallons of water a day, so are good for drinking and cooking only. And if there are significant particulate or dissolved metals, require pretreatment so they do not get fouled quickly.
This is actually true of all particle filters (but much more expensive for an RO unit) and so have some limits. An RO unit (reverse Osmosis will take out everything, including viruses, chlorides and sodium and will not add anything back.
RO units have massive use for treating municipal waste for reuse as drinking water (Orange County in California) with good effect, but theinitial cost of such units make home use prohibitive.
I will try to finish the treatment postings soon.