If the source is analogue and the processing chain is purely analogue, capture will be at the target rate (i.e. 44.1k for CD release) and a higher rate (i.e. 96k) for asset repurposing (e.g. Hi-res download or Pure Audio Blu-ray, or even for vinyl).
This is the same process employed with straight transfers and DSD.
If the source is analogue and the processing chain is mostly analogue but with a digital limiter at the capture end, and further editing is required, capture is always at 96k.
If the source is analogue but the processing chain is purely digital, capture will always be at 96k. All targets are generated from the 96k master (i.e. 48k for video and 44.1k for CD).
The quality of the SRC available today is much improved over what was available only a few years ago and I have no issue at all converting between "disparate" rates (e.g. 96k and 44.1k). I wouldn't hesitate using Saracon or iZotope or the newer Sonic SRCs.