My PC doesn't have a "line-in" jack - only USB and HDMI. How do I connect the stereo RCA output from my reel-to-reel deck to my PC to transfer the audio to the PC?
With a USB soundcard. If you don't need a microphone input, there are several pretty solid USB soundcards in quite affordable price range with line-level inputs to be had on the second-hand market. Just make sure that the driver situation with your PC is good. "Class-compliant" cards with USB 2.0 "high speed" connection are the best bet for stuff that is going to work without a lot of headaches for a variety of current and future systems.
I've banked on the combination of a solid minidisc desk (with A/D converters and digital outputs) and a cheap USB 1.1 sound-card with digital optical input myself at one time (with the rationale of "digital is lossless, so price doesn't matter once we are digital") but that was not a good scheme because of the dropouts.