Minimum voltage for DC amplifier
There is no real limit to amplifying even a sub pico-volt signal. Whether you can extract that signal from noise is a different matter entirely. The noise can be already present on your signal or, it can be added by the amplifier. For op-amps there are a couple of numbers in the data sheet that describes how much the amplifier adds noise.

Voltage noise density describes the effective power per hertz of bandwidth. A reasonable op-amp will have a figure like 10 nV per \$\sqrt{Hz}\$. This may seem confusing but if you square the voltage noise density and reference it to 1 ohm it becomes power per hertz. If you have a signal that can occupy a bandwidth of 20 kHz (i.e. audio) you take the square root of 20,000 (equals 141) and multiply that by the 10nV (=1.41\$\mu\$ volts). This is the equivalent RMS voltage at the input to your amplifier. If the amp has a gain of 1000, then the output noise is 1.41 milli volts RMS. To get a reasonable feel for this as a peak-to-peak signal, multiply it by 6.6. Why 6.6? It's all about the density of noise being gaussian in nature and multiplying by 6.6 means you have applied 6.6 standard deviations to a random signal in order to predict what the extremes are (within a confidence level of 99.9%): -



Another pointer to noise in the op-amp is low frequency peak-to-peak noise. It is specified differently to voltage noise density (above) because it is a different noise source. Normally this covers the frequency range 0.1Hz to 10Hz and is specified in \$\mu\$ volts p-p. If your frequency band of interest covers this area it has to be taken into account.

Current noise density is like voltage noise density except it defines what the bias current noises are from the input transistors. To convert to an equivalent voltage it is multiplied by the (external) source resistances in and around your input circuits.

And finally (probably), there is the noise of the resistors themselves. This is nothing to do with your amplifier. The voltage noise of a resistor is: -

\$\sqrt{4\cdot k_B\cdot T\cdot R\cdot \Delta F}\$

Where 


\$k_B\$ is Boltzmanns's constant
T is absolute temperature in kelvins
R is resistance in ohms
\$\Delta F\$ is the frequency range you are interested in.


For a 1k ohm resistor at normal ambient temperature (300K) it will produce a voltage noise density of about 4nV per \$\sqrt{Hz}\$.

And after you've calculated the three noise densities (voltage noise, current noise and resistor noise) you can add them all together by using \$\sqrt{A^2 + B^2 + C^2}\$ to get an equivalent input noise. I always treat the 0.1Hz to 10Hz noise as a separate entity and don't mix it in with the three noise densities just mentioned.