Firstly, yes they can be a bit (electrically) noisy due to the switching - this might be noticeable if you rely on the full accuracy of the ADC for example. You will save power though.Secondly if you want to run at low power then the standard Arduino won't really help you as the USB<->serial chip is consuming power all the time, whether or not you power-down the microcontroller. This can be 15 or 20mA or so (about the same as the Arduino microcontroller itself). It might be better to consider a board like the Mini or Pro Mini which doesn't have the USB chip, and is available in 3V3 / 8MHz versions (significantly lower power consumption, and sleeping the chip has a definite effect)If you are only interested in periodic monitoring of the battery then spending most of the time in sleep state will help a lot. Look around these forums for how to setup sleep state, there are a couple of libraries at least to make this relatively painless.Little 12 -> 5V and 12 -> 3.3V switchmode supply modules aren't _too_ pricey, more than a linear regulator - however they may not handle sleep mode well (some are better than others at being efficient at low-loads - though this is also true of linear regulators).The keyword "micropower" is a good one to add to your search in this context.
Regulating to 5V from 12V, you've got 7V across the regulator and 5V across the load. And since they both share the same current (with a linear regulator), the regulator is wasting more power than your curcuit is utilizing! And, it's actually worse than that, since "12V" lead-acid batteries actually charge-up to 14.4V. (With a switching regulator, you get-out more current than goes-in.)
An option which may or may not work for you is to utilize the built-in constant voltage reference (1.1V I think? and maybe other available options depending on which AVR chip you're using?) and redesign your voltage divider to scale the AGM battery's voltage down to that range. Might be more stable.As far as power feeding into your arduino goes, I highly recommend using proper decoupling (capacitors and probably multiple ones of differing values, e.g. 0.01uF along with 10uF) connected between GND and the output of your switching power supply OR linear regulator to help stabilize things.