The order of processing the prerecorded samples (DC removal, Hilbert transform, frequency shifting)
Order of operations can be changed but will change where the processing is applied and that may be simplified in certain conditions which will be very obvious once the actual signal is processed if the goals of each step are understood. For example, if the OP means by DC a non-zero carrier (which will appear at DC after moving the signal completely to baseband), this is much easier to remove after moving to baseband by simply subtracting the mean. However in actual applications, the carrier may not initially be perfectly estimated, in which case a tone close to DC will occur and subtracting the mean will be ineffective (but the tone can be used to continue to refine the carrier estimate).  If the OP meant the waveform itself as received prior to any processing has a large DC offset, this too can be removed prior to any processing with a simple subtraction of the mean (since the samples are pre-recorded this would be simplest) assuming the DC offset is not desired for some reason, otherwise the tone it becomes will be filtered out regardless in the subsequent processing below. (There can of course be advantages to removing the DC signal first in terms of dynamic range available but that would all be clear in the specicic procssing done and precision of the operations.
No Hilbert transform is necessarily needed, if the frequency initially is at a carrier sufficiently higher than its bandwidth, simply frequency translate the real signal to baseband using using $e^{-j\omega_c t}$ which means feed the signal into to multipliers and multiply one with $\cos(\omega_c t)$ and multiply the other with $\sin(\omega_c t)$ to get a complex I and Q output and filter the remaining higher frequency component that will reside at $e^{-j 2\omega_c t}$ (this is a typical Digital Downconverter (DDC) architecture).
For further details of this approach, please see:
https://dsp.stackexchange.com/a/51280/21048