Note that you can't get wideband noise in a single stage from 1k+ gain. To cover the audio band, you need a 20MHz GBW amp to do that.
A quad of even a slacker jellybean amp (e.g. LM324?) offers more than enough GBW in a package to achieve this though. Set each stage for the same gain.
ST's LM324 datasheet says 40nV/rtHz, which is line level (0.775Vrms) in the audio band (20kHz) for a total gain of 0.775V / (40nV/rtHz * sqrt(20,000 Hz) ) = 137k. (Considering the LM324 minimum gain at DC is only 25k, you can see why multiple stages are a must!) The 4th root is 19.23, the amount of gain per stage required. So, four inverting-gain-of-20 stages will do just fine. The actual bandwidth to expect is GBW / gain, or 1.3MHz / 19.23 = 67kHz, which should be more than enough. In fact, the RMS output will be about 1.83 times too high at this natural bandwidth; use a 20kHz lowpass to fix this.
Particularly in older amps like LM741, beware of excess noise such as 1/f and popcorn noise. I don't know offhand how much of this is a problem with other types. Bipolar amps do tend to exhibit a lower 1/f knee than JFET amps, but it's still within the audio band. For best results, calibrate the source.
All this assuming the filters you're testing are even audio band, which you didn't mention...
Tim