The classical low noise In-amp is the AD620 (about 1/5 the noise of the AD623). However one has to check the supplies and common mode range.
An important factor is the source impedance and the frequency range of interest. The noise figure depends on the source impedance and thus different amplifier are good at low and high impedance.
A second amplification stage is far less critical. So the AD623 would be well good enough. If going with OPs the MCP6002 could be just good enough. However there are other options, at low frequency even an LM358 may be better, though not rail to rail.
Rail to rail is tricky anyway as the input stage cross over can cause quite some error. So the really useful input range is often limited even with RR OPs
. One could consider something like TLE2021 or LT1013 if price does not matter.
200 kHz would be a totally different ball park and would need much faster amplifiers.