I've waited a while to comment. I'm not a historian, but am an environmental engineer and urban planning grad student, my research being on water utility planning and management. That said, while I can't point you to the best historical/archaeological sources or go into detail about the progression of the technology date/era wise, I can tell you what water engineers are taught about our Roman antecedents. A lot of useful information, especially diagrams, can be found here[1] One thing to note is that the basic Roman urban drinking water supply approach is not really very different at a macro-level from modern systems. If you took a Roman engineer in a time machine and showed them say, Denver's water system, they'd basically get it. The basic idea is illustrated here[2]
On the left is the water source. This is always some way to get water from the environment. Water quality starts here. The roman's had basically 4 ways of doing this (as do we). River Intakes-Basically you build a pipe submerged in a river and make the pipe go where you want, as long as overall it's going down hill (Super oversimplification here) the water will flow. Spring Boxes (see Figure 1 here[3] The basic idea is you dig a hole and line it with concrete except for some purpose built openings that allow water from an underground spring to get in. The water stays in the container and allows sediment to settle to the bottom before more clear water goes through an outflow pipe to wherever you've designed it to go) Dams - dams were compratively rare in roman hydraulic engineering, but were used in some places. You build a dam, and then it's easy to basically stick a pipe in the dam, or build a small part of the dam to divert part of the river flow to an open aqueduct Infiltration Galleries - This is very common as far as I can tell in roman waterworks. Basically you run a porous pipe (or just a long rectangular structure) made out of gravel or bricks or even just big rocks that can be packed together in a hillside or under a river bank. Groundwater seeps in through the rocks and then goes where you direct it. Now, of these methods, spring boxes and infiltration provide a sort of filtering mechanism, and dams and spring boxes provide a sedimentation mechanisms. These can help to clean the source water. River water was generally known to be of high contamination risk. Vitruvius (an architect under Caeser and Augustus) wrote about it in Book 8 his treatise De Architectura, although book 8 is pretty jumbled and shows poor understanding compared to the other parts. Now, having covered source water quality, which could vary depending on the water itself and the source structure type, the water was transported in aqueducts, which were generally stone or clay pipes underground for most of the way to the city. Sometimes they were exposed to the air. The aqueducts that fed Rome itself were covered when they were above ground to protect them from contaminants and also to keep the water cool. For Rome itself, each of the main aqueducts feeding the city (I forget their names off the top of my head) came from a different source, and were known to be of varying water quality. The aqueducts known to have the best quality water were used for drinking water. The qqueducts would feed into large settling basins (big chambers of water that lower its flowrate enough for sediments to float to the bottom, another cleaning mechanism). This was called the Castellum divisorium Sometimes these also had more advanced things like charcoal filters. Anyway, this is where you might pour your poison, but they weren't the most accessible things. Drinking water was distributed by lead, clay, or stone pipes coming out of the settling basins and distributed to continuously running public taps/ baths throughout the service area. If you were a normal person, this is where you got your water. It was for the most part reasonably clean coming out of the pipe, although not up to modern, western water quality standards. Waterborne disease was probably still a problem, though. Sometimes, the settling basins would have separate chambers, each feeding into a pipe system that fed the baths, public taps, and private home systems respectively. Oh yeah, that answers another question. Rich people could get piped water to their house. It would come out of a spout int he wall into a small basin. Like a big sink with the tap on all the time. Ah! running out of time. A nice overall source to look at if you can find it is Hodge, A. Trevor. Roman aqueducts & water supply. Vol. 2. London: Duckworth, 1992. Not sure about intraurban water politics in ancient Rome, but it happens now in poor countries all the time, where the basic municipal water system is designed pretty much the same.